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TIME POINT-LEVEL ANALYSIS OF

TRANSIT SERVICE RELIABILITY AND PASSENGER DEMAND

by

THOMAS JEFFREY KIMPEL

A dissertation submitted in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY in

URBAN STUDIES

Portland State University 2001

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ABSTRACT

An abstract of the dissertation of Thomas Jeffrey Kimpel for the Doctor of Philosophy

in Urban Studies presented May 4, 2001.

Title: Time Point-Level Analysis of Transit Service Reliability and Passenger Demand

Considerable effort is being expended by transit agencies to implement

advanced communications and transportation technologies capable of improving

transit service reliability. Improvements in transit service reliability will produce

benefits for both passengers and operators. Routes characterized by unreliable service

may have difficulty attracting new riders or suffer patronage declines over time.

Increased wait times at stops result in higher travel costs, which ultimately influence

mode choice decisions. Transit systems with poor service quality require additional

fiscal resources because of higher operating and capital costs. For both transit

providers and passengers, the primary issue is that there are monetary costs associated

with unreliable service.

This research uses archived Tri-Met Bus Dispatch System data relating to bus

transit performance and passenger activity, along with socioeconomic and land use

information to analyze transit service reliability and passenger demand at the time

point (route-segment) level of analysis. Observations refer to individual trips

summarized over 19 days for 5 radial and 2 crosstown routes. The sample was

stratified by route typology and time period, with the radial peak period models further

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stratified by direction. In order to more closely approximate the experience of

passengers, the bus performance variable is differentiated according to time period of

operation.

The findings of the transit service reliability models suggest that efforts to

control delay at early points along a route will produce benefits to passengers in the

form of more reliable service. Factors found to contribute to delay variation include

the amount of delay variation at the previous time point, passenger demand variation,

link speed variation, and distance. The findings of the transit patronage models

suggest that socioeconomic and land use characteristics are more important

determinants of demand than factors that are directly under the control of the transit

agency.

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TABLE OF CONTENTS

DEDICATION i

ACKNOWLEDGEMENTS ii

LIST OF TABLES vi

LIST OF FIGURES vii

Chapter 1 INTRODUCTION 1

1.1 General Background 1

1.2 Research Objective 3

1.3 Empirical Analysis 4

1.3.1 Data 4

1.3.2 Multiple Linear Regression Models 5

1.3.3 Applications of Research 6

1.4 Overview of Dissertation 6

Chapter 2 GENERAL BACKGROUND 8

2.1 Introduction 8

2.2 Transit Service Reliability 8

2.3 Temporal and Spatial Dimensions of Transit Service 13

2.4 Empirical Analysis of Transit Service Reliability 14

2.5 Empirical Analysis of Passenger Demand 19

2.6 Expected Relationships Between Variables 25

2.6.1 Simultaneity Between Demand, Supply, and

Service Quality 25

2.6.2 Route-Level Demand Models 26

2.6.3 Time Point-Level Demand Models 31

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2.7 Level of Aggregation 35

2.8 Simultaneity Considerations 37

2.9 Chapter Summary 38

Chapter 3 DATA INTEGRATION 40

3.1 Introduction 40

3.2 Analysis Framework 41

3.2.1 Sampling Frame 41

3.2.2 Study Routes 41

3.2.3 Data Structure 48

3.3 BDS Data Collection 51

3.4 Spatial Data Consistency 55

3.5 Database Integration 57

3.6 Transit Service Areas 59

3.7 GIS Allocation 61

3.7.1 Limitations of the Uniform Density Method 62

3.7.2 Competing Service Areas 64

3.7.3 Improved Time Point Service Area Allocation

Methods 65


Chapter 4 EMPIRICAL ANALYSIS 71

4.1 Introduction 71

4.2 Operational Models 71

4.2.1 Transit Service Reliability 72

4.2.2 Passenger Demand 77

4.3 Empirical Results 82

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4.3.1 Introduction 82

4.3.2 Results: Radial Reliability Models 83

4.3.3 Results: Crosstown Reliability Models 92

4.3.4 Results: Radial Demand Models 98

4.3.5 Results: Crosstown Demand Models 103

4.4 Modeling Issues 108


Chapter 5 DISCUSSION AND CONCLUSIONS 113

5.1 Introduction 113

5.2 Applications 113

5.3 Discussion 116

5.3.1 Transit Service Reliability Models 116

5.3.2 Passenger Demand Models 119

5.4 Directions for Future Research 121

5.5 Contributions 124

REFERENCES 127

APPENDICES 134

Appendix A: Sample Data Set 134

Appendix B: Descriptive Statistics 137

Appendix C: Model Elasticities 144

Appendix D: Time Point Observations 146

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LIST OF TABLES

Table Page

2.1 Summary Level Categories 35

3.1 Study Route Characteristics 43

3.2 Data Structure Example 49

3.3 Allocation of Employment to Time Point Service Areas 67

4.1 Description of Variables: Transit Service Reliability Models 72

4.2 Operational Models: Transit Service Reliability 73

4.3 Description of Variables: Passenger Demand Models 77

4.4 Operational Models: Passenger Demand 78

4.5 Results: Radial Transit Service Reliability Models 84

4.6 Results: Crosstown Transit Service Reliability Models 94

4.7 Results: Radial Passenger Demand Models 99

4.8 Results: Crosstown Passenger Demand Models 104

4.9 Heteroskedasticity: Comparison of Corrected and Uncorrected T-scores 110

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LIST OF FIGURES

Figure Page

2.1 Comparison of Route Time Point-Level Models 33

3.1 Location of Study Routes 42

3.2 BDS Data Collection Process 52

3.3 Sample Output of BDS Card Data 54

3.4 Spatial Data Consistency 56

3.5 Controlling for Existing Levels of Delay 56

3.6 Database Integration 58

3.7 Time Point Service Area Definition 61

5.1 Interpretation of Delay Variation at Previous Time Point Coefficient 115

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CHAPTER ONE

INTRODUCTION

1.1 General Background

Considerable effort is being expended by transit agencies to implement

advanced communications and transportation technologies capable of improving

transit service reliability. Improvements in transit service reliability will produce

benefits for both passengers and operators. Improved schedule adherence at bus stops

will reduce the variability of bus arrival times and lower average passenger wait times.

A decrease in arrival time variability will allow schedulers to remove excess recovery

time built into schedules. This will free up resources for use elsewhere or negate the

need for additional buses. Improved headway regularity will reduce bus bunching,

lower average passenger wait times, and ensure that vehicle capacity is utilized

efficiently. For both transit providers and passengers, the primary issue is that there

are monetary costs associated with unreliable service.

Unreliable service is caused by a number of factors that can be classified as

either endogenous or exogenous to the transit system (Woodhull, 1987). Endogenous

factors include passenger demand variation, route configuration, stop spacing,

schedule accuracy, and driver behavior. Exogenous factors include traffic congestion

and accidents, traffic signalization, on-street parking, and weather conditions.

Recurring problems such as traffic congestion can be dealt with via scheduling.

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Nonrecurring problems such as vehicle breakdowns and traffic accidents add an

additional level of complexity to the management of the system in real time.

Strategies to improve transit service reliability are typically classified as either short-

or long-term strategies (Abkowitz, 1978; Turnquist 1978; Woodhull, 1987). Short-

term strategies involve returning service to schedule through operations control and

include such actions as vehicle holding, short turning, leap frogging, and bringing

additional vehicles into service. Long-term strategies involve structural changes and

include schedule modification, route reconfiguration, and driver training programs.

Transit patronage models provide a basis for service planners to analyze the

impacts of proposed service changes to assist in budget preparation and other resource

allocation decisions. Service reliability is important to transit service planning in that

it is related to the level of transit subsidy. Transit systems with poor service quality

require additional fiscal resources because of higher operating and capital costs. The

amount of subsidy influences the budget which ultimately determines level of service

(Tisato, 1998). Another justification for why transit service reliability is important to

service planning is that unreliable service directly affects passenger wait times.

Bowman and Turnquist (1981) found that wait time at stops is much more sensitive to

schedule reliability than service frequency. Increased wait times result in higher travel

costs, which ultimately influence mode choice decisions. Routes characterized by

unreliable service may have difficulty attracting new riders or suffer patronage

declines over time. Transit service reliability is an important measure of service

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quality and directly affects both passenger demand and level of service (Abkowitz,

1978).

1.2 Research Objective

This research provides a framework for analyzing transit service reliability and

estimating passenger demand at the time point level of analysis. Time points are

specific point locations on bus routes from which vehicles are scheduled to depart at

specified times (Tri-Met, 1993). Time points are typically spaced about 1.5 miles

apart, with buses serving approximately 8-12 stops per time point. Time points are of

particular importance to analysis of transit service reliability at Tri-Met because the

published schedule is written to time points and forms the basis for analyzing

operating performance. The analysis begins with a literature review of empirical

research pertaining to transit patronage modeling and transit service reliability analysis

and shows how advances in transportation technologies are producing vast amounts of

data that encourage the use of new modeling techniques. Differences between route

level and time point-level models are discussed. It is shown that a number of

problems exist with time point-level demand modeling that prevent the use of

simultaneous equations estimation, and that ordinary least squares (OLS) regression

estimation is more appropriate. The data requirements for time point-level modeling

necessitate a complex spatial database integration scheme. The results of the

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passenger demand and transit service reliability models are presented along with a

discussion of policy implications.

1.3 Empirical Analysis

1.3.1 Data

Tri-Met, the transit provider for the Portland, Oregon metropolitan region,

implemented the automated Bus Dispatch System (BDS) in the fall of 1996. The BDS

is based upon the integration of several technologies including (a) an automatic

vehicle location (AVL) system that uses global positioning system (GPS) technology

to track buses in space and time, (b) a computer-aided dispatch (CAD) and control

center, (c) a two-way radio system allowing voice and data communication between

operators and dispatchers, and (d) automatic passenger counter (APC) technology.

The BDS collects a considerable amount of information related to bus operations for

each vehicle in the system. Information derived from the BDS serves two

fundamentally different purposes within the transit agency. First, BDS information

pertaining to bus location and operator communication is utilized in real time for

purposes of operations control. Second, BDS information is archived and used for a

variety of different purposes including performance monitoring, service planning, and

scheduling.

This research uses archived BDS data relating to transit performance,

passenger activity, and non-recurring events along with socioeconomic and land use

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information derived from a geographic information system (GIS) to analyze transit

service reliability and passenger demand. The data cover 19 days of weekday bus

operations comprising 5 radial and 2 crosstown routes. The study sample is stratified

according to route typology and time period. Radial peak period models are further

stratified by direction. Only the primary direction of travel is considered in radial

peak models.

1.3.2 Multiple Linear Regression Models

The models developed in this analysis employ multiple linear regression.

Multiple linear regression is an appropriate statistical technique for answering research

questions that seek to explain values of the dependent variable in relation to a number

of predictor variables. Each regression coefficient measures the amount of change in

the dependent variable associated with a unit change in the independent variable,

holding all other explanatory variables at their mean values. The underlying

hypothesis is that the regression coefficient is not different from zero and hence, has

no influence on the dependent variable. OLS regression and simultaneous equations

estimation techniques have been used in previous studies of passenger demand and

transit service reliability.

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1.3.3 Applications of Research

Several applications are developed from the regression model coefficients.

The models provide insight into the determinants of transit service reliability and

passenger demand at the time point level of analysis. Sensitivity analysis is

undertaken for key policy variables derived from the models, enabling transit analysts

to better understand the potential effects of various decisions on bus transit demand

and service reliability.

1.4 Overview of Dissertation

Chapter Two presents a summary of previous research undertaken in the areas

of bus transit passenger demand and transit service reliability. It begins with a

discussion of the most common measures of transit service reliability and shows that

transit providers and transit patrons view service reliability differently. Previous

empirical studies in the areas of transit service reliability and transit patronage are

described. Differences between route and time point-level modeling are discussed in

relation to the expected theoretical relationships between variables in a simultaneous

system of equations. It is shown why single equation multiple linear regression

models are more appropriate than simultaneous equations models at the time point

level of analysis.

Chapter Three pertains to data collection and integration. The chapter begins

with a description of the sampling frame and the selection of study routes. The

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technological aspects of BDS are discussed in relation to the integration of several

advanced transportation and communications technologies. The BDS data collection

process is described in detail. A spatially consistent bus performance database is

necessary for analysis of passenger demand and transit service reliability at the time

point level of analysis. Socioeconomic and land information data are allocated to

transit service areas using a GIS. Examples of two complex allocation procedures are

presented.

The study design is presented in Chapter Four. The chapter begins with a

discussion of the operational models. Formal models are presented for time point-

level analysis of transit service reliability and passenger demand. Descriptions of the

variables used in the analysis are given. The results of the empirical models are

presented. Problems frequently encountered using OLS regression estimation are

discussed.

The findings from the empirical models are discussed in Chapter Five. In

particular, the findings are discussed in relation to their relevance to service planning,

scheduling, and operations control, as well as from the perspective of passengers.

Various applications of the models are presented and a number of improvements to the

models are suggested. Directions for future research are given and the conclusions of

the study are presented.

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CHAPTER TWO

GENERAL BACKGROUND

2.1 Introduction

Advances in automated data collection technologies such as those used by the

BDS provide new opportunities for analyzing transit service reliability and passenger

demand in a more detailed and comprehensive manner than previously possible. This

is because data are now being collected on a continuous basis and at much finer spatial

and temporal resolutions. This section begins with a discussion of transit service

reliability and highlights several problems with measuring bus performance. A

detailed literature review of bus transit passenger demand and transit service reliability

models is presented. The review shows that simultaneity is likely to exist between

transit service reliability, service supply, and passenger demand at the system level.

However, an in-depth look at previous research shows that the rationale behind

simultaneous equations estimation is largely contingent on the use of aggregate data.

2.2 Transit Service Reliability

Transit service reliability is a multidimensional phenomenon in that there is no

single measure that can adequately address service quality. The most common

measures of transit service reliability typically relate to schedule adherence, running

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times, and headways. The usefulness of each service reliability measure is largely

determined by service frequency, whether or not timed transfers must be met, and

functional need (e.g., scheduling or performance monitoring). Important distinctions

exist between passengers and operators in their perceptions of service quality.

Departure delay (actual departure time minus scheduled departure time)

effectively measures schedule adherence for a given bus at a particular location.

Schedule adherence is an important reliability measure for infrequent users, timed

transfers, and service characterized by large headways. Traditionally, transit agencies

use on-time performance (OTP) as a key measure of schedule adherence. The

majority of transit agencies define “on time” as a bus arrival (departure) of no more

than 1 minute early and 5 minutes late (Bates, 1986). OTP is a discrete measure that is

particularly useful for evaluating system reliability from the perspective of the transit

agency. OTP is expressed at the percentage of buses that depart a given location

within a predetermined range of time. The on-time window represents an acceptable

range of delay tolerance that takes into account the fact that buses operate in a

stochastic environment. In contrast, the use of a continuous measure like departure

delay is more consistent with how passengers actually experience delay. Adhering to

a strict definition of OTP is problematic from the perspective of passengers because all

early and late departures are considered to be of equal consequence. The regional

transit agency in Toronto is the only transit provider known to categorized late

departures according to severity of delay (Toronto Transit Commission, 1986).

Another promising area that has yet to be explored concerns dynamic scheduling

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where different schedule adherence policies are set according to time of day

(Levinson, 1991).

Headway delay (actual headway minus scheduled headway) effectively

measures the spacing between buses. A negative value for headway delay means that

a bus is falling behind its leader, with a positive value meaning that a bus is gaining.

Extreme variation in headway delay results in bus bunching. As a bus falls behind

schedule, the spacing between it and the previous bus becomes larger, resulting in

greater passenger loads that cause additional delay. The following bus experiences

lighter passenger loads and thus tends to gain on its leader. This dynamic process

tends to propagate as vehicles progress along a route. Bus bunching represents a poor

use of agency resources since uneven passenger loading can require the use of

additional vehicles to serve the same number of passengers. The impact of uneven

headways on passengers are twofold: (a) Overloaded buses might result in passengers

being passed up due to lack of available seating, and (b) average wait times increase

when service becomes highly variable.

Running time is also an important measure of transit performance. Running

time represents the elapsed time for a bus to traverse from one location to another.

Running-time delay (actual running time minus scheduled running time) measures

how well a bus is moving along each link. A positive value of running-time delay

means that a bus is having difficulty traversing the link. Running time is an important

measure of bus performance to transit providers because it serves as key scheduling

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input and provides a means for monitoring schedule accuracy. Running times are

important to passengers to the extent that they affect OTP and in-vehicle travel time.

Transit agencies concerned with improving service quality from the

perspective of passengers should focus on reducing the variability of bus performance

over time (Abkowitz, 1978). If a bus is consistently 2 minutes late, passengers simply

learn to time their arrival with that of the bus. Passengers would consider the bus

reliable because it operates in a predictable manner. If a bus departs 5 minutes late

one day and 1 minute early the next, passengers are forced to arrive at stops much

earlier in order to compensate for highly variable departure times. In this case, the bus

service would be considered unreliable. A caveat is that passengers' perceptions of

service quality are at least partially related to service frequency. One finding from a

passenger survey conducted by Tri-Met prior to BDS implementation was that

passengers were more likely to express satisfaction with the performance of bus routes

that operated at high frequencies, though subsequent analysis showed that these same

routes were among the least reliable (Tri-Met, 1996). This apparent dichotomy exists

because passenger wait times are still relatively small on high frequency routes with

poor service reliability, compared to better performing routes that operate less

frequently.

While passengers are primarily concerned with day-to-day variability in bus

performance, transit planners and schedulers are typically interested in measures of

bus performance pertaining to longer periods of time. Several months or a year’s

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worth of operations data are typically summarized in route performance reports and

passenger censuses.

Many researchers have argued that bus performance should be measured at

intermediate locations along a route rather than at the route terminus because

relatively few passengers are affected at terminal locations (Woodhull, 1987;

Henderson, Adkins, & Kwong, 1990; Nakanishi, 1997). It is more practical for

agencies to monitor transit service reliability at peak load point or at regularly spaced

intervals such as time points. According to Abkowitz (1978) and Koffman (1990),

passengers are mostly concerned with schedule adherence at their particular bus stop.

Koffman argues that each bus stop should be considered when designing schedules in

order to provide the best possible service to passengers. A schedule that provides

adequate running time over the course of the route yet permits buses to run either early

or late over most time points is indicative of a poor schedule. At present, few transit

agencies have the ability to monitor service quality or set schedules at the bus stop

level.

It is important to make a distinction between low- and high frequency service

when discussing transit service reliability. For routes characterized by infrequent

service or those with timed transfers, schedule adherence is the most important

reliability measure. Passengers attempt to time their arrivals with that of the bus based

upon a given probability of missing the departure (Turnquist, 1978; Bowman and

Turnquist, 1981). Under these circumstances, average wait times are less than one-

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half of the scheduled headway. High frequency service is typically defined as bus

service that operates at headways of 10 minutes or less (Oliver, 1971; Abkowitz,

Eiger, & Engelstein, 1986; Abkowitz & Tozzi, 1987; Wilson, Nelson, Palmere,

Grayson, & Cederquist, 1992; Nakanishi, Y.J., 1997). For routes that operate at high

frequencies, headway variability is the most important reliability indicator. The

aggregate wait time of passengers is minimized when buses are evenly spaced.

Because passengers do not find it advantageous to time their arrivals with that of the

schedule on high frequency routes, an assumption of random passenger arrivals is

valid.

2.3 Temporal and Spatial Dimensions of Transit Service

Tri-Met operates a multi-destinational transit system within the Portland

metropolitan region. The goal of Tri-Met's service design is to provide good service

to downtown as well as non-downtown locations (Tri-Met, 1989). The service design

is based upon an urban grid system in more densely developed areas and a timed-

transfer system in the lower density suburbs. The grid system consists of radial and

crosstown routes operating at relatively high frequencies. Radial routes link suburban

and urban locations to downtown. Radial routes either have a terminus in downtown

or continue in the opposite direction as radial through routes. Crosstown routes serve

non-downtown trips between urban neighborhoods. Transit centers are often located

at suburban activity centers and are linked with downtown via high frequency trunk

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lines. Feeder lines serve the low density suburbs and connect to transit centers and

trunk lines. Feeder lines often consist of small buses or paratransit operations. Tri-

Met operates radial and crosstown routes with standard sized buses that seat

approximately 35-40 passengers.

It is well known that transit service varies over time, space, direction, and by

route typology (Abkowitz & Engelstein, 1983; Abkowitz & Engelstein, 1984; Stopher,

1992; Strathman & Hopper, 1993; Peng, 1994; Hartgen & Horner, 1997). Areas with

high population and employment densities tend to generate greater amounts of

ridership than their lower density counterparts. Locations such as transit centers, park-

and-ride lots, and transfer points are often associated with large patronage volumes.

Temporally, a considerable amount of variation in demand exists on bus routes over

the course of a single day. The highest levels of ridership coincide with the

concentration of work trips during peak time periods of operation. Demand on radial

routes is not directionally balanced during the morning and afternoon time periods.

Passenger demand is greater in the inbound direction during the a.m. peak time period

and lighter in the outbound direction. The opposite holds true for travel during the

p.m. peak time period. Peak period demand on crosstown routes is typically not

differentiated by direction.

2.4 Empirical Analysis of Transit Service Reliability

Surprisingly few econometric models have been developed analyzing the

determinants of bus transit service reliability. The only econometric study known to

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explicitly address schedule adherence was a multinomial logit model developed by

Strathman and Hopper (1993) that analyzed factors affecting the OTP of buses in

Portland, Oregon. A discrete measure of OTP was used that defined "on-time" as a

bus departing a time point no more than 1 minute early or 5 minutes later than

scheduled. The model analyzed the relative probabilities of on-time/early, on-

time/late, and early/late bus departures. Variables included the number of boardings

and alightings, the number of stops since the previous time point, the position of the

time point in the sequence of time points, distance since previous time point,

scheduled headway, and dummy variables consisting of weekday service, peak period

service, part-time driver, and new sign-up period. The study found that the probability

of a bus arriving on-time was adversely affected by the number of alighting

passengers, the size of the scheduled headway, time point in sequence of time points

(cumulative distance), part-time driver, and new sign-up period.

A number of investigators have noted that route characteristics are important

determinants of transit service reliability (Turnquist, 1978; Guenthner & Sinha, 1983;

Woodhull, 1987; Abkowitz & Engelstein, 1984; Levinson, 1991, Strathman &

Hopper, 1993). Route characteristics may include such factors as scheduled distance,

the number of scheduled stops, the number of signalized intersections, and on-street

parking. Bus performance tends to deteriorate with increases in any one of these

variables.

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Several researchers have noted that driver experience and behavior are

important factors affecting transit service reliability (Abkowitz, 1978; Woodhull,

1987; Levinson, 1991; Strathman & Hopper, 1993). Driver behaviors that may

adversely affect bus performance include not departing from the terminal on time,

making unscheduled stops, or spending excess dwell time at stops. Drivers can

positively influence bus performance by modifying vehicle speed and stopping

activity in response to schedule adherence and bus spacing problems. A study

comparing OTP before and after BDS implementation showed significant

improvements in OTP by simply providing real-time schedule adherence information

to operators (Strathman, Dueker, Kimpel, 1999). An important aspect of the empirical

analysis by Strathman and Hopper is that they attempted to control for the effects of

driver experience and behavior on bus performance. A dummy variable representing

the first two weeks of a new sign-up period was used to control for adjustments in

behavior following changes in route assignments. A dummy variable representing

part-time driver was also included because it was thought that part-time drivers either

lack experience in general or may be unfamiliar with a particular route.

Two empirical studies by Abkowitz and Engelstein examined factors affecting

vehicle running times on two radial bus routes in Cincinnati, Ohio, using OLS

regression techniques. Each route was divided into a series of 1-3 mile links. The

first study sought to explain mean running time. The results showed that mean

running time on individual links was affected by link distance, the number of

boardings and alightings, the number of signalized intersections, the percentage of the

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link where peak period parking was allowed, and time period (Abkowitz & Engelstein,

1983; Abkowitz & Engelstein, 1984). Route-segment length was found to be the most

important variable affecting mean running time, followed by the number of signalized

intersections and the number of boarding and alighting passengers. Relatively few

econometric studies have attempted to control for effects of vehicular traffic on bus

performance, though traffic is commonly believed to adversely impact service quality

(Welding, 1957; Sterman & Schofer, 1976; Turnquist, 1982, Levinson, 1991).

Normal traffic conditions including congestion, traffic signalization, and the amount

of time taken to merge back into traffic can be controlled for via scheduling. The most

important traffic-related factor affecting bus performance is non-recurring traffic

congestion. Schedules are designed to take into account a small degree of running-

time variation, yet it is not cost effective for transit agencies to account for excess

levels of congestion.

Passenger activity is widely believed to be a cause of unreliable service

(Woodhull, 1987; Abkowitz & Engelstein, 1983; Abkowitz & Engelstein, 1984;

Strathman & Hopper, 1993). According to Woodhull (1987), the effect of load

variation on bus performance is largely a function of the location of the peak

passenger load point. For inbound radial routes in the a.m. peak time period, the

maximum load point is often located just outside the central business district (CBD).

This means that bus performance is adversely affected by demand variation only over

the last portion of the route. For outbound radial routes during the p.m. peak time

period, the maximum load point is often the CBD. Radial through routes present an

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interesting case in that any delay variation introduced on the inbound portion of the

trip will propagate in the outbound direction if insufficient recovery time is provided

or if schedules are poorly written. Demand variation is likely to adversely impact

transit service reliability on crosstown routes due to transfer activity to and from radial

routes.

The second running-time model by Abkowitz and Engelstein addressed

cumulative running-time deviation. Cumulative running-time deviation at the

previous location was used to control for existing levels of unreliability. Route

segment length and running-time deviation at the previous location were shown to

have adverse effects on cumulative running-time deviation (Abkowitz & Engelstein,

1983). The authors also undertook an analysis of headway variation. Using data

derived from a Monte Carlo simulation, the authors modeled the effects of running-

time variation and scheduled headway on headway variation. The study found that

headway variation increases sharply near the beginning of a route, then reaches an

upper bound (Abkowitz & Engelstein, 1984). According to the authors, the length of

time taken to reach the upper bound is dependent upon the size of the scheduled

headway and the amount of running-time variation. This finding highlights the

importance of controlling for the amount of scheduled service in analysis of transit

service reliability because of its relationship to the amount of delay variation.

Random events such as traffic accidents and weather can adversely affect bus

performance (Woodhull, 1987). The effects of inclement weather are indirect in that

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they influence bus performance through traffic-related problems. Random events that

are likely to cause delays include those related to emergencies, mechanical failure,

passenger behavior, traffic incidents, and driver-related problems. No transit service

reliability studies are known to exist that have taken any of these sources of delay into

account.

With the exception of the OTP model by Strathman and Hopper and the mean

running-time model by Abkowitz and Engelstein, the majority of transit service

reliability models rely on rather simplistic model specifications. The reason for such a

paucity of well designed econometric models is primarily due to data limitations.

Traditionally, manual data collection efforts proved to be costly, time consuming, and

of limited duration. Advanced transportation and communications technologies, such

as BDS, now generate geographically-detailed bus operations data on a continuous

basis. Though a number of transit agencies make use of AVL technology, relatively

few have implemented AVL systems capable of collecting and storing data for

subsequent service quality monitoring and analyses (Mueller & Furth, 2001).

Archived bus operations data present new opportunities for analyzing transit service

reliability in a more detailed and comprehensive manner than previously possible.

2.5 Empirical Analysis of Passenger Demand

A number of econometric models have been developed analyzing the

determinants of bus transit demand. Passenger boardings are typically modeled as a

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function of level of service, route characteristics, and various socioeconomic and land

use variables. The majority of models have been developed at the route level of

analysis except for route segment level models developed by Peng (1994) and

Pendyala and Ubaka (1999). The transit patronage models developed by Peng

represent the most advanced empirical work to date. The analysis by Pendyala and

Ubaka serves as a useful validation of Peng's research but does not add to the existing

body of theory. Peng estimated a series of route segment-level models stratified by

time of day and direction for bus routes in Portland, Oregon. Route segments were

delineated by fare zone. Passenger demand was estimated as a function of transit

service supply, population, downstream population, employment density, alightings

from complimentary routes, ridership on competing routes, park-and-ride capacity,

fare zone, and route typology. Service supply was estimated as a function of current

ridership, previous-years ridership, population, employment density, and route

typology. A third equation was included to control for the effects of competing routes

on ridership. Competition between routes occurs where two or more routes that

service the same destination have overlapping service areas (Peng 1994). Peng

showed that bus routes do not operate independently from one another and that a

service change on one route will impact demand on another. The results of Peng's

research show that service supply, population, employment density, income, and park-

and-ride capacity are significant determinants of bus ridership. Route typology, fare

zone, and inter-route effects were found to vary in importance between models. In the

supply equation, current ridership, previous-years ridership, population, and

21

employment density were found to be important. The dummy variables for route

typology also varied in significance between models. The most notable aspects of

Peng's research are the development of route-segment level models and the use of

simultaneous equations estimation to control for the feedback effects between supply,

demand, and route competition.

Kemp (1981) estimated a route-level simultaneous equations model using

pooled time series/cross-sectional data. Five structural equations were employed,

including two for demand (transfer and non-transfer passengers), two for supply

(average headway and seat miles operated) and one for service quality (average bus

speed). The demand equation for transfer passengers estimated transfer rides as a

function of total patronage, number of transfer opportunities, route typology, and time

trend. Boardings was used as an instrumental variable. All of the explanatory

variables in the model proved significant. The signs on the coefficients were positive

except for the single- and double-branch radial route typology variables which showed

an adverse effect on the demand for transfer passengers. The demand equation for

non-transfer passengers estimated passenger trips as a function of fare price, a proxy

for auto travel costs, average bus speed, expected wait time, hours of service, route

length, stop spacing, number of school days, and other factors. The analysis found

that non-transfer passenger demand was negatively associated with fare price, stop

spacing, route length, and the particular route of operation. Demand was found to be

positively associated with service duration, the proxy variable for auto costs, number

of school days, time trend, and bus route. Neither average bus speed nor the wait time

22

variable was found to be significant in the demand equation. The research by Kemp is

important in that it makes a distinction between demand resulting from transfer and

non-transfer passengers and is the only known study to include aspects of service

quality in a passenger demand model.

The basis of transit service planning is to match service levels with passenger

demand subject to budgetary and policy considerations. Because demand is closely

related to the amount of service provided on a route, the majority of transit patronage

studies include an explanatory variable related to service quantity. Both Peng (1994)

and Azar and Ferreira (1994) used the number of scheduled seats in the time period as

an endogenous service supply variable in the demand models. The variable takes into

account not only the frequency of service but also the seating capacity of buses. Two

bus routes with different seating capacities operating at the same service frequency

provide different levels of service. Other studies have used transit service supply

variables relating to the mean number of buses per hour (Stopher, 1992), mean

scheduled headway (Pendyala and Ubaka, 1999), and seat miles operated (Kemp,

1981). At the very least, the service supply variable should be related to frequency of

service, the duration of the service period, and seating capacity where appropriate.

Nearly all passenger demand models include one or more variables related to

the size of the transit market. Bus routes that serve areas characterized by high

population and employment density are likely to experience greater levels of ridership

(Kyte et al, 1988; Stopher, 1992; Peng, 1994; Hartgen & Horner, 1997; Pendyala &

23

Ubaka, 1999). The demand for transit is not only determined by the characteristics of

the originating area but also by the attractiveness of the destination (Multisystems,

Inc., 1982; Horowitz, 1984; Azar and Ferreira, 1994). In the absence of origin-

destination information on passengers, other variables can proxy for destination

attractiveness. Peng (1994) included a variable, downstream population, to control for

downstream attractiveness in the outbound direction models. In passenger demand

modeling, it is necessary to control for additional sources of patronage. The most

common sources of additional passengers include transferring passengers (Kemp,

1981; Multisystems, Inc, 1982; Horowitz & Metzger, 1985; Peng, 1994), high school

students (Kemp, 1981; Peng, 1994), and park-and-ride users (Multisystems, Inc.,

1982; Peng, 1994). In metropolitan areas, a significant number of high school

students use public transit to travel to and from school. Most transit agencies are

aware of this fact and add extra bus trips to serve students in the morning and

afternoon time periods. Publicly-owned park-and-ride lots are often located adjacent

to transit centers. Transit centers are also associated with a large number of

passengers transferring between radial, crosstown, and feeder routes. Significant

transfer activity also occurs at the intersections of radial and crosstown routes.

A number of studies have shown that income is an important determinant of

transit ridership (Algers, Hanson, & Tegner, 1975; Peng, 1994; Hartgen & Horner,

1997). Income is an important variable in passenger demand modeling because it

serves as a proxy for transit-dependent riders. Peng (1994) used a variable related to

the number of households with a median household income less than $25,000. Other

24

studies have shown that areas with high levels of auto ownership are typically

associated with lower levels of transit use (Algers et al, 1975; Levinson & Brown-

West, 1984). Other studies have sought to control for differences in fare price (Algers

et al, 1975; Kemp, 1981; Kyte et al, 1988; Peng, 1994; Hartgen & Horner, 1997).

Several researchers have discussed problems resulting from data limitations in

passenger demand modeling (Kemp, 1981, Multisystems, Inc., 1982; Azar & Ferreira,

1994). Deficient data result in the specification of overly simplistic models or force

the use of crude proxy variables in place of more desirable measures. A number of

researchers ignored the effect of competing routes on transit demand. Nearly all

previous research relies on patronage volumes derived from passenger censuses or

data collected for Federal Transit Administration Section 15 reporting. Prior to APC

implementation, Tri-Met used to conduct passenger censuses every 5 years at a cost of

approximately $250,000 to the agency. The passenger census involved manually

collecting stop-level passenger activity information for each bus trip in the system.

Section 15 reporting involves sampling a limited number of trips to produce ridership

figures that are statistically valid at the system level. In all cases, the number of

sampled trips is relatively small compared to the actual number of trips operated over

the course of a year. As APC deployment becomes more ubiquitous, the number of

sampled trips will increase, producing more reliable ridership estimates at much finer

spatial and temporal resolutions. One of the main benefits of disaggregate data is that

they can be aggregated according to the needs of each individual project.

25

2.6 Expected Relationships Between Variables

2.6.1 Simultaneity Between Demand, Supply, and Service Quality

Previous researchers have addressed simultaneity between transit demand,

service quantity, and competing route effects at the route-segment level of analysis

(Peng, 1994) and transit demand, service quantity, and service quality (average bus

speed) at the route level of analysis (Kemp, 1981). The relationship between demand

and service quantity is expected to be positively reinforcing. Over time, an increase in

passenger demand will likely result in additional service provision in the form of extra

bus trips. The service quantity increase should serve to lower average wait times,

resulting in a further increase in passenger demand. The increase in passenger

demand will cause service quality to deteriorate due to more highly variable boarding

and alighting activity. Bus routes characterized by poor service quality will likely

suffer patronage declines over time or have difficulty attracting new riders because

passengers are inconvenienced by unpredictable service. The overall effect is that the

initial increase in demand due to increased service provision will be partially offset by

a demand decrease due to adverse impacts on bus performance.

If bus performance deteriorates over time, more bus trips are required to serve

the same number of passengers. Bus routes with service reliability problems usually

receive additional resources in the form of extra buses. As more bus service is added

to a route, bus performance will likely improve because the amount of scheduled

service sets an upper bound on the level of service unreliability. At the same time, a

26

decrease in service reliability will likely have an adverse impact on passenger demand.

The initial decrease in reliability will be partially offset by an increase in reliability

resulting from lower patronage volumes.

2.6.2 Route-Level Demand Models

The following system of equations describes a hypothetical relationship

between demand, service quantity, and service quality at the route level of analysis:

(2.1) ),...,( XSRSQfD rrrr =

(2.2) ),...,( YSRDfSQ rrrr=

(2.3) ),...,( ZSQDfSR rrrr =

where (Dr) is the number of passenger boardings attributed to the route of interest,

(SQr) is the quantity of service provided on the route, (SRr) is a measure of service

reliability such as headway variation or departure delay variation, (Xr) is a vector of

socioeconomic and land use variables explaining passenger demand, (Yr) is a vector of

route and service characteristics explaining service quantity, and (Zr) is a vector of

route and operator characteristics explaining transit service reliability.

The dependent variable in the demand equation (2.1) typically represents the

average number of daily boardings on a route for a given period of time. For example,

a single observation might show 400 boardings for Route 15, inbound direction,

27

midday time period. Aggregating information that takes place at the stop level to the

level of individual route has important implications for demand modeling. As data are

aggregated to the route level, a considerable amount of information is lost. Route-

level observations assume that boardings are uniform along the entire length of the

route. In reality, demand varies considerably over the course of a route. Aggregating

boardings to the level of the individual route also makes it difficult to precisely control

for the effects of socioeconomic and land use characteristics on ridership.

The dependent variable in the supply equation (2.2) is a measure that takes into

account both service frequency and seating capacity. With a seating capacity of 40

persons per bus, a bus route operating 2 buses per hour for 4 hours results in a measure

of service quantity of 320 seats. It is important to note that the quantity of service is

typically not provided uniformly over time and space. It is often the case that a route

operates several different service patterns such as limited, short line, and express

service and that headways are not uniform throughout the time period. One way to

develop a more accurate measure of service quantity at the route level is to measure

service quantity at each time point for all bus trips associated with a given period of

time, then average over all time points. For example, a short line service pattern might

constitute 2 buses an hour over the first 4 time points, then 1 bus an hour over the last

2 time points. Assuming a 4-hour time period, the first 4 time points are served by 8

bus trips, and the last 2 time points are served by 4 bus trips. With a seating capacity

of 40 persons per bus, the total amount of service provided on the route in the time

period is approximately 267 seats or roughly 67 seats per hour. As long as changes in

28

service patterns are predominately associated with time points, this type of calculation

results in a reasonably accurate measure of the amount of service provided on a route.

Such a method addresses the fact that the amount of transit service provided on a route

varies by spatial location.

Similar to most transit systems, Tri-Met sets peak period service frequencies

according to passenger volumes based upon loading standards. Service frequencies

are set by calculating the average number of passengers on board each bus, on a per-

minute basis, crossing the peak load point (Tri-Met, 1993). In off-peak time periods,

service frequency is set according to policy headways. Policy headways represent the

minimal headway under which transit service operates. Tri-Met sets policy headways

in off-peak time periods in a manner that ensures that every passenger has an available

seat. Accordingly, demand typically does not exceed seated capacity during off-peak

time periods. Because of the different standards for setting service frequencies in peak

and off-peak time periods, the strength of the relationship between transit supply and

demand should be stronger during peak time periods. The fact that peak period

service frequencies are set according to passenger loads raises an important issue in

demand modeling. This is because boardings are not representative of passenger

loads. Passenger loads are largely determined by the dynamic interaction of boardings

and alightings as buses proceed along a route. An important aspect of this process is

that the peak load point typically occurs at a single location along a route. Demand

models that use the number of boardings as an explanatory variable in the supply

29

equation are using a proxy variable in place of a more desirable variable relating to

passenger loads.

Because passengers are more concerned about the day-to-day variability in bus

performance, the dependent variable in the service reliability equation (2.3) should

represent delay variation. Headway delay variation and departure delay variation are

appropriate measures of transit service reliability for peak and off-peak service,

respectively. The researcher is confronted with the task of choosing a method for

calculating transit service reliability. Measuring transit service reliability at the route

terminus is not sufficient because relatively few passengers are affected by service

quality at terminal locations. A more logical place to measure service reliability is at

locations where the greatest numbers of passengers are affected, such as peak load

points (Woodhull, 1987; Levinson, 1991), or where service coordination is required,

such as key transfer points (Woodhull, 1987). A variable could be developed by

measuring the amount of delay variation at the peak load point, then summarizing over

all trips in the time period. The researcher may also choose to measure the amount of

delay variability at each time point, then summarizing over all trips in the time period.

Another option would be to develop a trip-level, passenger-weighted measure of

service reliability that takes into account both the volume of passenger activity and the

amount of delay at each bus stop, then aggregate the values over all trips in the time

period. Regardless of the method chosen, route-level demand modeling requires that

the performance measure be assigned to the whole route. The difficulty of calculating

a meaningful transit service reliability variable is perhaps one of the reasons why

30

many previous researchers have not used a service quality measure as an explanatory

variable in route-level demand modeling or have not found it to be a significant

determinant of passenger demand.

A more serious problem with the service reliability equation concerns the use

of passenger boardings as an endogenous variable. Headway and departure delay

variation are better explained by boarding and alighting variation, rather than the mean

or total number of boardings. In the interests of retaining the use of passenger

boardings as an endogenous variable in a simultaneous equations model, the number

of passenger boardings would need to serve as a crude proxy for both boarding and

alighting variation.

Researchers confronted with the task of developing route-level transit

patronage models are faced with a number of interesting problems. Most of the

problems are due to inherent differences in the spatial and temporal characteristics of

transit demand, supply, and service quality. The precision of the service quality and

service reliability variables can benefit from information collected below the route

level. A reasonable method for dealing with temporal differences in transit service is

to use information pertaining to individual bus trips, then aggregating to the time

period. Spatial issues are considerably more complex. Demand is realized at the level

of the individual bus stop, yet is assigned to the whole route. Service quantity is

typically set at the route segment level based upon differential loading standards that

vary by time of operation or by policy considerations. Peak period service frequencies

31

are set according to the passenger volumes passing the maximum load point. The

maximum load point occurs at a single location on each route. In order to maintain

consistency between the dependent variable in the demand equation and the passenger

activity variable in the supply equation, the researcher would have to use the number

of boardings in place of a load-based variable in the supply equation. Service

reliability is relevant at the level of the individual bus stop because this is where

passenger activity occurs. The actual form of the passenger activity variable presents

a serious problem for route-level demand modeling using simultaneous equations

estimation. This is because the passenger activity variable needs to capture the effect

of boardings in the demand equation, passenger loads in the supply equation, and

boarding and alighting variation in the reliability equation.

2.6.3 Time Point-Level Demand Models

At the time point level of analysis, the notion of simultaneity between demand,

service quantity, and service quality breaks down upon closer inspection. The key

difference between route and time point-level demand modeling concerns the effect of

moving down in spatial scale from the route to the time point. On the surface, the time

point appears to be a more appropriate unit of observation for addressing simultaneity

between passenger demand, service supply, and service reliability. This is because the

time point is closer in spatial scale to real world conditions. There are three

fundamental spatial scales at which transit operates. These scales represent routes,

32

time points (route segments), and stops. Both passenger demand and transit service

reliability are relevant at the level of the individual bus stop. Service frequencies are

typically set at the time point level.

At the time point level of analysis, each variable is assigned to an individual

time point rather than a whole route. The top portion of Figure 2.1 shows hypothetical

values for certain key variables assigned to Route 15, inbound direction, midday time

period. The bottom portion of Figure 2.1 shows hypothetical values for the same

variables assigned to Route 15, inbound direction, midday time period, TP 4. In the

example, 400 average daily boardings are assigned to the level of the individual route.

At the time point level, 60 boardings are assigned to TP 4. Values for other time

points may be considerably higher or lower depending upon the boarding profile of the

route. The main point is that there will be considerable variation in the number of

boardings associated with each time point over the course of a route. This is crucial

for understanding the relationship between passenger demand, service supply, and

service reliability at the time point level of analysis. At the route level, the amount of

delay variability attributed to a route is considered uniform over the course of the

route. The example shows an average value of headway delay variation of 6.4

minutes for the route. At the time point level, the example shows 8.2-minutes

headway delay variability at TP 4. Similar to demand, there is likely to be

considerable variation in the amount of delay attributed to each time point.

33

P 5 TP 4 TP 3 TP 2 TP 1 TP 0

Route Level Boardings: 400 boardings Scheduled seats: 288 seats Headway delay variation: 6.4 minutes Peak load point (PLP): 33 passengers Time Point Level Boardings: 60 boardings Scheduled seats: 320 seats Headway delay variation: 8.2 minutes Peak load point: 33 passengers Figure 2.1 Comparison of Route and Time Point-Level Models

T

PLP

PLP

The values for headway delay variability will likely be lower at earlier time points

along the route and higher at downstream locations. This is because delay variability

introduced at early points along a route tends to become progressively worse as

distance along the route increases. At the time point level of analysis, the relationship

between delay variability and passenger demand is weak. In many cases, there will be

time points associated with large amount of delay variability yet little passenger

activity. This often occurs when passenger demand is heavy at early points along the

route then tapers off towards the end of the route. At the other end of the spectrum,

there will be time points where there are large amounts of passenger activity yet low

levels of delay variability. This phenomenon makes it difficult to isolate the effects of

delay variability on passenger demand. The important point to remember is the

34

impact of delay variability on passenger demand at the time point level cannot be

viewed in isolation from the boarding profile of the route.

The example presented in Figure 2.1 provides additional insight into the

differences between route and time point-level demand modeling. The example

assumes a short-line service pattern operating a 30-minute headway over the first 4

time points and a 60-minute headway over the last time point for a 4-hour time period.

At the route level, 288 scheduled seats are provided in the time period. At the time

point level, the amount of scheduled service is 320 seats over the first 4 time points

and 160 seats over the last time point because of the service pattern change. Note that

there are 400 boardings associated with a service quantity of 288 seats at the route

level and only 60 boardings associated with a higher quantity of service at the time

point level. The only time points that exhibit a close relationship between supply and

demand are those containing the peak load point and those subject to a pattern change.

This has important implications for time point-level demand modeling. There will be

time points with relatively high levels of service yet low levels of passenger demand.

Even if multiple service patterns were provided in relation to varying levels of

demand, the relationship between supply and demand would still be tenuous. The

lesson is that service pattern changes can affect the supply of transit service at each

time point, but not in a manner that can precisely match supply with demand over all

time points. In moving the scale of analysis from the route to the time point, it

becomes apparent that the relationship between supply and demand is not as strong as

that occurring at the route level.

35

2.7 Level of Aggregation

Modern data collection systems such as BDS generate substantial amounts of

data in disaggregate form. Depending upon the objectives of each study, disaggregate

data can be summarized in a number of different ways. Table 2.1 shows three general

categories of summary levels grouped by transportation feature, service attribute, and

time. The most common summary items for analysis of transit operations are shown

within each category.

Table 2.1 Summary Level Categories

Summary Level Item Transportation Feature Route, route segment, time point, bus stop, service area Service Attribute Route typology, pattern, train (block), trip, operator Time Annually, quarterly, daily, time period, and day type

There are tradeoffs involved in using one level of aggregation over another. Previous

researchers have used the total number of boardings attributed to a route over the

course of a month (Kemp, 1981) or the average number of daily boardings attributed

to a route segment (Peng, 1994) as the dependent variable in demand equations. It is

commonly understood that the demand for transit is time, direction, and location

specific. The notion that the demand for transit is also trip specific has not been

explicitly addressed in previous research. Focusing on the level of the individual trip

captures the behavior of the majority of transit users who typically depart for

destinations at predetermined times. Rather than aggregating passenger activity over

all trips in a time period, this analysis focuses on trip-level observations. The

36

dependent variable in the demand models is thus the average number of daily

boardings over a time point for an individual bus trip (i.e., the same scheduled bus).

The main focus of this research is to explain the determinants of bus transit

service reliability and passenger demand at the time point level of analysis. Because

passengers are concerned about the day-to-day variability in bus service, the transit

service reliability models developed in this research focus on explaining delay

variation measured at time points. A distinction is made according to service

frequency with respect to the dependent variables used in the transit service reliability

models. For peak time period models, the dependent variable represents headway

delay variation. For off-peak time period models, the dependent variable represents

departure delay variation. In order to generate measures of variance, the bus

performance data are summarized over all days of observations. Theory suggests that

unreliable service pertains to individual trips and that the demand for transit is also

specific to individual trips. As such, the unit of observation in the research is a bus

trip departing a time point.

Schedules are designed to balance headways and passenger loads over all trips.

At first glance it does not seem like a variable representing transit service supply is

relevant in a demand equation where observations refer to individual trips.

Controlling for the amount of service provided at time point locations is important

because of the effect of service pattern changes on demand. A service supply variable

37

is also necessary in the transit service reliability equations because it serves to control

for the effect of the size of the scheduled headway on the amount of delay.

2.8 Simultaneity Considerations

Simultaneity is likely to exist between transit service supply and passenger

demand at the route level of analysis. This is particularly true when one is comparing

the aggregate number of boardings to the amount of service supplied on a route. The

consequences of ignoring simultaneity are severe in that the estimated coefficients are

biased and inconsistent. Furthermore, hypothesis tests on the parameter estimates are

invalid. Feedback effects between supply and demand are likely to diminish in

importance as one moves down in spatial scale from the route level to the time point

level. At the time point level, the only spatial locations where there is a strong

relationship between supply and demand are the time point containing the peak load

point and time points affected by service pattern changes. By focusing on the level of

the individual, supply is no longer an important determinant of demand, since

headways are given.

In order to test the supposition that the characteristics of demand are partially

contingent upon spatial scale and the particular summary level, correlation coefficients

were run between mean boardings attributed to a route, summarized over all trips in

the time period by direction and time of day (route-direction-time of day), and mean

boardings attributed to a time point summarized at the level of the individual trip by

38

direction and time of day (route-direction-time of day-trip-time point). The

correlation coefficients are 0.14 for radial routes and 0.23 for crosstown routes. The

low correlation coefficients suggest a weak relationship between route-level and time

point-level demand under different summary levels.

2.9 Chapter Summary

Advanced data collection systems such as BDS generate large quantities of

data that are used in real time and, once archived in a database, for advanced analysis

of transit operations. Detailed descriptions of the most common measures of transit

service reliability are presented along with their strengths and weaknesses. Passengers

and transit agencies view transit service reliability differently, with passengers more

concerned about the day-to-day variability in bus service. Previous studies of

passenger demand and transit service reliability are described in relation to existing

theory. It is shown that there are important differences between route and time point-

level demand modeling. At the route level of analysis, simultaneity is likely to exist

between demand, service supply, and service quality. This is particularly the case

when observations are aggregated over all trips in a time period. Simultaneous

equations estimation is problematic at the time point level of analysis due to spatial

inconsistencies in the relationships between demand, supply, and service quantity and

because of problems related to the form of the passenger activity variable between

equations. It is argued that separate OLS regression equations are more appropriate

39

for analysis of transit service reliability and passenger demand at the time point level

of analysis, particularly when using observations that refer to individual trips.

40

CHAPTER THREE

DATA INTEGRATION

3.1 Introduction

Spatial data integration is critical for advanced analysis of transit operations.

The analysis requires that all variables be related to a common geography. The basic

premise behind spatial data consistency is that the source data representing different

spatial units must be allocated and assigned to a common unit of observation (Peng &

Dueker, 1994; Peng & Dueker, 1995). The basic unit of observation in this research is

the time point. Source data were assigned to time points using a relational database

and a GIS. This chapter begins with a description of the sampling frame and the study

routes used in the analysis. The data structures for the transit service reliability and

passenger demand models are presented. Problems encountered during data collection

and data processing are discussed. BDS data collection is described along with some

of the uses of BDS information at Tri-Met. The database integration scheme is

presented along with a discussion of data sources. Allocation methods are developed

using disaggregate information to assign socioeconomic and land use information to

time points. Different allocation procedures are required depending upon whether the

variable of interest is in aggregate or disaggregate form. Route competition is

addressed during the allocation process.

41

3.2 Analysis Framework

3.2.1 Sampling Frame

The sampling frame covers 19 weekdays of bus operations from October 4

through October 29, 1999. The data are treated in a cross-sectional manner, with the

analysis limited to explaining the determinants of passenger demand and transit

service reliability for a given period of time. The models are appropriate for

addressing short-term changes in demand and service quality. The data were stratified

by route typology and time of day. The radial peak time period models were further

stratified by direction, with only the primary direction of travel considered. Tri-Met

recognizes the following time periods: a.m. peak (6 a.m.-9 a.m.), midday (9 a.m.-3

p.m.), p.m. peak (3 p.m.-6 p.m.), evening (6 p.m.-9:30 p.m.) and night (9:30 p.m-6

a.m.). The night time period was not analyzed in this research.

3.2.2 Study Routes

A total of 5 radial routes and 2 crosstown routes were used in the analysis. The

selection of study routes was based upon three principal factors: a continuation of

study routes analyzed in previous phases of the project; the need for representative

crosstown route typology; and the requirement that routes be served by APC-equipped

buses. The radial routes represented in the study consist of Routes 4, 8, 14, 15, and

104. The crosstown routes used in the study consist of Routes 72 and 75. Figure 3.1

shows the locations of the study routes.

42

Figure 3.1 Location of Study Routes

The study routes primarily serve North, Northeast, Southeast, and downtown Portland,

with service extending to the cities of Gresham, Milwaukie, and parts of Clackamas

County. The crosstown routes are shaped like an inverted "L" and connect the

Southeast part of the region with North and Northeast Portland. In the past, both

crosstown study routes consisted of 2 separate routes that were eventually connected

for purposes of operational efficiency. Each radial route is required to cross one of

several bridges over the Willamette River leading to and from downtown.

43

The following section provides a brief description of each study route including

information related to route characteristics such as typology, route length, and the

number of time points. Also included are descriptions of the primary operational

problems associated with each route and the land use and socioeconomic

characteristics of the surrounding area. Table 3.1 shows the general characteristics of

each of the study routes.

Table 3.1 Study Route Characteristics

Route Name Typology Distance (mi) TP (in ) TP (out ) 4 Fesseden Radial 10.1 6 6 8 NE 15th Radial 8.7 8 7 14 Hawthorne Radial 8.0 6 6 15 Belmont Radial 8.4 6 6 104 Division Radial 13.4 7 7 72 Killingsworth/82nd Crosstown 16.5 9 9 75 39th/Lombard Crosstown 17.0 10 10

Route 4-Fesseden represents one-half of a radial through route that provides

service from the St. Johns neighborhood to downtown Portland. The other leg of the

route, Route 104-Division, is also included in the analysis. Route 4 is approximately

10.1 miles in length has 6 time points in each direction. There are no major

operational issues associated with Route 4 outside of typical heavy loads during peak

time periods. Route 4 in the outbound direction has lower levels of OTP because the

inbound trip on Route 104 is sometimes delayed. St. Johns is a working class

neighborhood in North Portland with the University of Portland just to the South.

Route 4 serves a number of low- to medium-income neighborhoods in North and

Northeast Portland. Retail and commercial activity is limited to intersections of major

arterials. Route 4 intersects the Rose Quarter Transit Center that is served by

44

numerous bus lines and the MAX light rail line. Route 4 crosses the Willamette River

by way of the Steel Bridge. Route 4 serves the downtown Transit Mall, an exclusive

bus lane operating in downtown Portland.

Route 8-N.E. 15th represents one-half of a radial through route that operates

from Hayden Meadows to downtown Portland. Route 8 has 7 time points in the

inbound direction and 8 time points in the outbound direction. The route is

approximately 8.7 miles in length. Route 8 has no major operational problems except

for heavy passenger loads during peak time periods. Occasionally, high traffic

volumes near Lloyd Center adversely affect bus performance. Hayden Meadows is an

area containing big box retail outlets and sports facilities such as Portland Meadows

and the Portland International Raceway. Route 8 serves a number of low- to

moderate-income neighborhoods in North Portland. The portion of the route along

N.E. 15th from Broadway to just South of the Albina neighborhood is characterized by

middle to upper class housing. The route serves Lloyd Center which contains a large

urban shopping mall and a dense cluster of high rise buildings, many of which house

state and federal offices. Route 8 intersects the Rose Quarter Transit Center. The

route serves the downtown Transit Mall and crosses the Willamette River by way of

the Steel Bridge. Route 8 turns into Route 108 which serves a large medical complex

upon leaving downtown.

Route 14-Hawthorne provides service from the Lents neighborhood near S.E.

94th and Foster to downtown Portland. Route 14 is the only radial route in the

45

analysis that is not a through route. The route is approximately 8.0 miles in length and

has 6 time points in each direction. The main operational problem with Route 14 is

heavy passenger loads. Route 14 is a high frequency route that is subject to bus

bunching problems during peak time periods. The outer portion of the route from

about S.E. 50th onwards is predominately low-density residential development. The

Lents neighborhood is one of the lower income areas of the city. The portion of the

route along Hawthorne from S.E. 39th to S.E. 12th serves a popular urban

neighborhood characterized by dense multifamily housing and trendy shops and

restaurants. The area from S.E. 12th to the Hawthorne Bridge is known as the Inner

Southeast Industrial District and contains almost no housing. The Hawthorne Bridge

is the most active of all the Portland lift bridges. Similar to all of the other radial

routes, Route 14 serves the downtown Transit Mall.

Route 15-Belmont is part of a radial through route that runs from Gateway

Transit Center to downtown Portland. Route 15 is roughly 8.4 miles in length and has

6 time points in each direction. Route 15 does not have serious operational issues.

Gateway Transit Center is a major eastside transit center served by a number of bus

routes in addition to light rail. Gateway Transit Center is surrounded by a large

amount of retail development and contains a medium-sized shopping mall. There are

few residences in the area surrounding the transit center. A number of patrons are

commuters from Vancouver, WA, who use the transit center's park-and-ride facilities.

The portion of Route 15 that operates along S.E. Belmont from Mt. Tabor to S.E. 12th

is primarily single family residential development interspersed with clusters of retail

46

and commercial development. The Belmont neighborhood is characterized by higher

than average property values. Route 15 crosses through the Inner Southeast Industrial

District. The route crosses the Willamette River using the Morrison Bridge and serves

the downtown Transit Mall.

Route 104-Division is a radial route that operates on a major arterial street

from the Gresham Transit Center to downtown Portland. Route 104 is the longest

radial route in the study. The route has a length of approximately 13.4 miles and

contains 7 time points in each direction. There are no major operational issues

associated with Route 104 except for heavy loads during peak time periods. Route

104 in the outbound direction has lower levels of OTP because the inbound trip on

Route 4 is sometimes delayed. The Gresham Transit Center is located in downtown

Gresham. Three Tri-Met owned park-and-ride lots are located near the transit center

which serves as the terminus for the MAX light rail line. Route 104 serves

neighborhoods that are predominately single family residential with retail and

commercial development located at major intersections. The outer portion of the route

beyond S.E. 50th has more retail and commercial development and higher housing

values than the inner portion. Route 104 crosses the Willamette River by way of the

Hawthorne Bridge. Route 104 runs along the downtown Transit Mall and continues

on as Route 4-Fesseden into North Portland.

Route 72-Killingsworth/82nd is a crosstown route that runs from Swan Island

to Clackamas Town Center. Route 72 is a long route covering a distance of

47

approximately 16.5 miles with 9 time points in each direction. Route 72 consists of a

North/South segment along S.E. 82nd and an East/West segment along Killingsworth.

At one time, the two segments that comprise Route 72 were operated as separate

crosstown routes. Approximately one-third of the passengers travel from one leg of

the route to the other. Route 72 carries more passengers than any other route in the

Tri-Met system and is associated with a large amount of transfer activity. The major

operational problem associated with Route 72 is uneven passenger loading that is

particularly severe along S.E. 82nd. The portion of the route along 82nd contains a

large amount of retail and commercial development. The route terminates at the

Clackamas Town Center Transit Center. Clackamas Town Center is a large regional

shopping mall surrounded by a number of big box retail stores. Route 72 intersects

the MAX light rail line near Interstate 84. The East/West section of the route along

Killingsworth serves residential neighborhoods representing a mix of income classes.

There is little passenger activity from the Albina neighborhood to Swan Island. The

terminus of the route is Swan Island, an industrial area adjacent to the Willamette

River.

Route 75 is a crosstown route that runs from the City of Milwaukie to the St.

Johns neighborhood. Route 75 is the longest route in the analysis. It is roughly 17.0

miles in length and contains 10 time points in each direction. Route 75 has the second

highest ridership in the Tri-Met system. Unlike Route 72, few persons on Route 75

travel from one leg of the route to the other. Operational problems include heavy

passenger loads and a large amount of transfer activity. Both terminal locations are

48

largely working class neighborhoods. The S.E. 39th portion of the route terminates at

the Milwaukie Transit Center which serves a small downtown area. A number of trips

are shortlined before reaching Milwaukie because of lighter passenger demand. Land

use along 39th is mostly medium- to high-income residential neighborhoods with

clusters of retail and commercial development located at major intersections. Route

75 intersects the Banfield light rail line at the Hollywood Transit Center. The

Hollywood neighborhood contains above-average housing stock. The Lombard

portion of the route serves a mix of income types and is characterized by a high degree

of retail and commercial activity.

3.2.3 Data Structure

One of the main benefits of automated data collection systems such as the Tri-

Met BDS is that sufficient quantities of data are collected that allow for measures of

variability in bus performance over time and space. Each observation in the passenger

demand and transit service reliability models has a route, direction, trip, and time point

component (e.g., Route 14, inbound, trip 1080, time point 5). By default, the trip

number denotes time of day. The models use bus performance data summarized over

all days’ worth of observations with a minimum of three days required for inclusion in

the study.

Table 3.2 shows the data structure in more detail and highlights some of the

problems encountered during data processing. Route 14 is used as the example route

49

for purposes of discussion. The example shows 31 scheduled trips and 6 time points

for Route 14, inbound direction, a.m. peak time period. N(MAX) refers to the

maximum number of potential time point observations that could have been collected

under perfect conditions. N(TOT) refers to the number of valid observations available

for use in the study following data collection, processing, and cleaning. The number

of trips operated during a given time period is a function of the duration of the time

period and service frequency. For example, frequent service is provided in the p.m.

peak time period, yet the service period only lasts three hours. In contrast, the midday

time period operates at lower service frequencies but for a 6-hour period of time.

Because of the longer service period, the total number of trips is larger during the

midday time period.

Table 3.2 Data Structure Example

Obs. [Route] Dir. TOD Trips TP Days N (Max) N (Tot) RecoveryRaw [14] In 1 31 6 19 3,534 1,952 55.2% In 2 30 6 19 3,420 2,855 83.5% In 3 16 6 19 1,824 1,127 61.8% In 4 15 6 19 1,710 1,068 62.5% Out 1 17 6 19 1,938 1,530 79.0% Out 2 31 6 19 3,534 2,867 81.1% Out 3 27 6 19 3,078 1,373 44.6% Out 4 18 6 19 2,052 1,068 52.1% Total 21,090 13,840 65.6% Summarized [14] In 1 31 6 -- 186 162 87.1% In 2 30 6 -- 180 180 100.0% In 3 16 6 -- 96 96 100.0% In 4 15 6 -- 90 72 80.0% Out 1 17 6 -- 102 96 94.1% Out 2 31 6 -- 186 186 100.0% Out 3 27 6 -- 162 162 100.0% Out 4 18 6 -- 108 84 77.8% Total 1110 1038 93.5%

50

The first line in the table shows that 55.2% of the total number of potential

observations for Route 14, inbound, a.m. peak time period were successfully

recovered for use in the analysis. When summarized over all days of observations, the

recovery ratio increases. This can be seen in the bottom portion of Table 3.2. The

main implication of using summarized data in this research is that a number of

observations contain measures of variance calculated over a limited number of days.

These observations are likely to show greater variation compared to observations

which contain data summarized over more days.

If the missing observations have a systematic pattern, then sampling error may

occur. Table 3.2 shows that the a.m. peak, p.m. peak, and evening time periods all

contain a large percentage of missing time point observations. The primary reason

why observations fell out of the sample is because the majority of "tripper" buses were

not APC equipped. In general, trippers are older, non-APC-equipped buses that are

brought online during peak periods, make one or two trips on heavy demand routes,

then return to the garage. The agency operates a set number of buses on each route

throughout the day, with trippers inserted during peak periods to accommodate

demand on specific routes. The reason why the percentage of successfully recovered

observations in the midday time period is highest is because they operate regular

service, APC-equipped buses. One of the major limitations of APC deployment at

most transit agencies is that a considerable amount of passenger activity information is

lost on routes that are supposedly APC equipped due to trips being served by non-

APC-equipped buses during peak time periods. The majority of operational problems

51

are encountered during peak time periods. Failure to collect passenger activity

information on each bus in the system hampers bus performance monitoring and

analysis. There is no a priori reason to believe that APC-equipped buses perform any

differently than non-APC-equipped buses. In the event that there are differences, the

implication for sampling error due to non-APC-equipped buses is somewhat mitigated

by the study design which differentiates models according to time period of operation.

Other reasons observations fell out of the sample include post-processing

irregularities; database problems such as losing the reference trip needed to calculate

headways; trips lost because of operators laying over before the end of the trip; and

time constraints on the part of the database programmers which resulted in the evening

time period being truncated on certain routes where extensive pattern changes

occurred. Approximately 87,500 time point observations (62.5% of all potential

observations) were recovered from the archived bus operations data prior to

summarization. Of the potential number of summarized observations, 85.3% of the

observations were successfully retained for use in the analysis. A sample of the

database is included in Appendix A.

3.3 BDS Data Collection

The Tri-Met bus fleet is 100% AVL equipped and 50% APC equipped. The

AVL system provides dispatchers with real-time information about the location of

each bus in the system with automatic updates occurring approximately every 90

52

seconds. Dispatchers also receive information from operators about events (attention

requests) either by voice communication or through pre-coded messages sent by radio

over data channels. Similar to most North American APC systems, Tri-Met's APC

technology is not capable of transmitting passenger count and load information in real

time (Levinson, 1991). The primary uses of APC data at Tri-Met are for planning,

scheduling, performance monitoring, and report generation.

There are a number of steps involved in BDS data collection (Figure 3.2).

Figure 3.2 BDS Data Collection Process

Data Collection

On-Board Computer

Data Card

Analysis / Reports

Relational Database

Schedule Matched

Uploaded to Network

BDS records information at the level of the individual train. A train is often referred

to as a block by other transit agencies. A train is a predetermined set of bus trips for a

given vehicle. Train numbers are used by Tri-Met to identify each bus in the sequence

of buses on a given route. A bus trip refers to a one way segment of service. The data

collection process starts at the beginning of each service day when an operator inserts

a data card containing the vehicle's schedule information into the vehicle control head

connected to the onboard computer. The vehicle control head displays real-time

schedule adherence information to operators and allows them to send pre-coded

53

messages to dispatch. Each time a stop or an event occurs, a data record describing

bus location, passenger activity, or communication is written to the data card. At the

end of each day the data card is removed and the information is uploaded to a central

computer where it undergoes schedule matching and validation. The information is

ultimately stored in a relational database and used for transit operations support.

The data collected by BDS contains a wealth of information on bus operations

(Figure 3.2). The data output contains bus and operator identification information

including date of operation, train, direction, trip, vehicle ID, operator ID, and stop ID.

BDS collects information on arrive time, depart time, and dwell time at each stop,

including unscheduled stops. Each bus stop in the Tri-Met system is locationally

referenced by a 30-meter stop circle in the agency's GIS system. Arrive time refers to

the time that a bus first enters the 30-meter stop circle except when a door opening

occurs. If a door opening occurs within the stop circle, then arrive time is overwritten

with the time of the door opening. This allows BDS to capture dwell time which is

measured as the amount of time elapsed from door opening to door closing. Departure

time refers to either the time of door closing or the time when a bus leaves the 30-

meter stop circle. BDS flags all door openings and lift operations. On vehicles

equipped with APC units, passenger activity information relating to boardings,

alightings, and vehicle loads are recorded. BDS also collects information relating to

the maximum speed of the vehicle since the previous stop and geographic coordinate

information (not shown).

54

BUS= 2132 TRAIN= 3507 DATE=20001214 BADGE= 6329 STOP ID STOP NAME ARRIVE LEAVE ON OFF MI D L DWEL SPD LOD 9573 NORTH TERMINAL (AT) 16:46:00 16:55:02 2 1 7 3 0 126 21 1 Scheduled times --------> 16:51:00 16:52:00 9302 5TH & HOYT (OP) 16:55:14 16:55:16 0 0 0 0 0 11 1 9222 5TH & EVERETT (NS) 16:55:44 16:56:36 1 0 1 1 0 7 13 2 9303 5TH & COUCH (NS) 16:57:28 16:58:10 0 0 1 0 0 10 2 7627 5TH & OAK (NS) 16:59:12 16:59:28 0 0 3 2 0 8 16 2 Scheduled times --------> 16:57:00 16:57:00 0 unscheduled stop 16:59:30 17:01:46 7 1 1 2 0 66 13 8 7642 5TH & WASHINGTON (NS) 17:01:48 17:02:10 0 0 1 0 0 13 8 7625 5TH & MORRISON (NS) 17:02:20 17:02:34 0 0 1 2 0 11 12 8 7640 5TH & TAYLOR (NS) 17:02:34 17:04:12 8 0 3 1 0 24 13 16 7614 5TH & MAIN (NS) 17:04:18 17:05:36 6 1 2 2 0 42 20 21 Scheduled times --------> 17:05:00 17:05:00 7594 5TH & COLUMBIA (NS) 17:05:58 17:06:58 3 0 1 2 0 23 35 24 3761 MARKET & 4TH (NS) 17:07:34 17:08:32 1 0 3 1 0 9 16 25 3760 MARKET & 2ND (OP) 17:09:00 17:10:04 2 0 1 2 0 15 12 27 6479 1ST & HARRISON (NS) 17:10:30 17:11:00 1 0 2 1 0 8 26 28 6483 1ST & LINCOLN (NS) 17:11:14 17:12:08 1 0 1 1 0 17 22 29 Scheduled times --------> 17:10:00 17:10:00 6473 1ST & MADISON TOWER (AT) 17:12:14 17:12:48 0 0 1 0 0 22 29 10480 SHERIDAN & NAITO (NS) 17:13:14 17:13:18 0 0 1 0 0 16 29 10468 NAITO PKWAY & ARTHUR (AT) 17:13:34 17:14:06 2 0 1 1 0 12 24 31 3120 KELLY & WHITEAKER (FS) 17:15:46 17:15:52 0 0 5 0 0 26 31 2797 HOOD & GAINES (NS) 17:16:16 17:16:24 0 0 2 0 0 27 31 3612 MACADAM & HAMILTON CT (OP) 17:17:20 17:17:38 0 1 5 1 0 4 33 30 3615 MACADAM & JULIA (FS) 17:17:58 17:18:26 1 0 2 1 0 5 27 31 time=17:18:28; Fare Evasion. 3604 MACADAM & BOUNDARY (NS) 17:18:38 17:19:24 0 2 2 1 0 6 26 29

Figure 3.3 Sample Output of BDS Card Data

Tri-Met writes schedules to departure times at time points. Time points are shown in

Figure 3.3 as "scheduled times" followed by an arrow. Scheduled departure times at

non-time point locations are interpolated using an algorithm based upon speed and

distance from the previous time point. Stop records are automatically recorded at each

bus stop regardless of whether or not any passenger activity occurs. Stop records are

also automatically generated for unscheduled stops. Figure 3.3 shows an unscheduled

stop occurring at arrive time 16:59:30. BDS collects approximately 500,000 weekday

stop records. Event records are recorded at various locations along a route whenever

55

an operator initiates communication with dispatch. Typical event categories relate to

emergencies, delays, passenger problems, mechanical problems, and operator needs.

Figure 3.3 shows a fare evasion event occurring at time 17:18:28. BDS generates

approximately 25,000 event records each day.

3.4 Spatial Data Consistency

The passenger demand and transit service reliability models developed in this

analysis require that all data be related to a unit of observation representing a time

point. The data correspond to three different types of spatial measurement: point,

polygon, and cumulative since previous time point. Figure 3.4 shows these different

types of measurement in more detail. Bus performance is measured at the individual

time point [A]. Both headway delay and departure delay are measured at time points.

Data associated with individual bus stops such as passenger boardings and the lift

operations are summed over all stops associated with a time point segment and

assigned to the time point [B]. These represent cumulative variables measured from

the previous time point. Socioeconomic and land use information such as income and

population are associated with time point service areas [C]. A time point service area

represents the market area served by bus stops associated with a particular time point.

In the example shown below, all data are spatially referenced to TP 4, the time point

of interest. By employing a common spatial data structure, the unit of observation is

the same for all variables used in the analysis.

56

B. Socioeconomic data measured here (polygon)

A. Bus performance data measured here (point)

TP 5 TP 4 TP 3 TP 2 TP 1 TP 0

Figure 3.4 Spatial Data Consistency

C. Stop-level data measured from previous time point (cumulative)

In theory, the amount of delay at a particular time point is a function of

everything that happens to a bus since it left the route origin. A variable measuring

the amount of headway variation at the previous time point or departure delay

variation at the previous time point can be used to control for existing levels of delay.

Abkowitz and Engelstein (1983) utilized a similar measure in their analysis of bus

running-time deviation.

Figure 3.5 Controlling for Existing Levels of Delay

A. Delay measured here

B. Delay at previous time point measured here

TP 5 TP 4 TP 3 TP 2 TP 1 TP 0

C. Time point service area

In the example shown in Figure 3.5, delay is measured at TP 4 [A]. Controlling for

the amount of delay at the previous time point [B] negates the need for cumulative

57

distance variables measured from the route origin. All other variables are associated

with the time point of interest [C]. Since bus performance tends to deteriorate with

increases in distance or running time, a measure of delay variation at the previous time

point negates the need for cumulative variables that are likely to be strongly

correlated.

3.5 Database Integration

A relational database is necessary for advanced analysis of transit service

reliability and passenger demand. Figure 3.6 shows the database integration scheme

used in this analysis. The integrated bus performance database requires information

from four separate data sources. The AVL/APC database consists of spatial and

temporal information on archived bus operations and passenger activity occurring at

each stop by date and train. The schedule database contains information referencing

route, direction, trip, scheduled depart time, and stop ID information. Bus

performance measures at time points were calculated after matching the AVL/APC

database with the schedule database. Event data, recorded at variable locations by

date and train, were linked with operations data based upon time of occurrence and

assigned to the nearest stop. Operator characteristics were joined with the operator ID

for a given train and referenced to individual trips. The integrated bus performance

database contains all of the necessary information required for time point-level

analysis of transit service reliability.

58

GIS Database [block group, tax parcel]

Event Database [date, train, time, XY]

Operator Database [date, train]

AVL/APC Database [date, train ,time, stop]

Schedule Database [route ,dir., trip, time, stop]

Integrated Bus Performance

Database [time point]

Passenger Demand Analysis

Service Reliability Analysis

Figure 3.6 Database Integration

Passenger demand analysis requires additional socioeconomic and land use

information obtained from a GIS database in addition to the bus performance data.

Block group-level socioeconomic and land use data from the 1996 American

Community Survey (ACS) were assigned to transit service areas using GIS allocation

techniques. Multnomah County, Oregon, was included as part of an ACS

demonstration project. The ACS is based upon a 3% annual survey of the population

with a 5-year rolling average used in final tabulations. Because 1996 represents the

first year that the survey was implemented, a 15% sample was conducted simulating 5

years’ worth of data. Information from the 1990 census were used for block groups

located outside of Multnomah County. The socioeconomic and land use information

59

used in the analysis included population greater than 16 years of age, employment, the

number of households, and the number of zero auto-ownership households.

GIS data were obtained from Tri-Met and the Regional Land Information

System (RLIS) maintained by Metro, Portland's regional government. The relevant

GIS coverages include the street network, bus stop, bus route, tax lot, employment,

and census block group layers. The employment data consists of 1995 Bureau of

Economic Analysis job count tabulations that were updated in 1996 and geocoded by

Metro for use in regional transportation models. A database file generated by

Multnomah County on the number of multifamily housing units was joined with the

tax lot coverage based upon the unique record number associated with each tax parcel.

The success rate for matching the multifamily housing unit database with tax lot

coverage was 88.3%. Most of the unsuccessful matches were associated with the

cities of Milwaukie and Gresham, two areas not covered in the multifamily housing

unit database. In these areas, missing values for the number of multifamily housing

units were imputed by dividing tax parcel value by $100,000. All tax parcels zoned as

single family residential were assigned a housing unit value of one. Because the ACS

data refer to 1996, the tax lot data were truncated to year built less than or equal to

1996.

3.6 Transit Service Areas

Accessibility to transit is typically defined using measures of distance or time.

A transit service area is defined as the geographic area surrounding a transit stop from

60

which patronage is derived (Lutin, Liotine & Ash, 1981). The standard distance used

in most transit research is a walking distance of one-quarter mile (USDOT, 1979a;

USDOT, 1979b). This value represents the maximum distance that the majority of

people are willing to walk to use transit. There are a number of different ways to

define transit service areas. One common method is to use Euclidean (straight line)

distance to buffer individual transit stops. Buffering transit features using Euclidean

distance is problematic in that it does not take into account the most likely path that

people take to use transit which is along sidewalks adjacent to the street network. The

method also ignores barriers to movement such as highways and rivers, and retains

areas that have no reasonable access to transit along the street network. Euclidean

distance buffering tends to overestimate the extent of transit service areas and thus the

number of patrons likely to frequent a given route. In light of the problems associated

with Euclidean distance buffering, a number of recent studies used distance along the

street network to define transit service areas (O’Neill, Ramsey & Chou, 1992; Zhao,

1998; Pulugurtha, Nambisan & Srinivasan, 1999). This analysis also uses street

network distance to define transit service areas because it more closely resembles the

behavior of transit users.

Time point service areas were created using a search routine based upon a

0.25-mile street network distance from each transit stop. Barriers to movement such

as freeways and access ramps were eliminated from the street coverage. Figure 3.7

shows how time point service areas were created in more detail. For purposes of

clarity, only two time point service areas are shown in the example. Bus stops are

61

A. Intermediate stop buffers

B. Time point buffers

Figure 3.7 Time Point Service Area Definition

represented by circles, and time points by squares. The search routine generated a

transit service area for each individual transit stop [A]. All stop buffers associated

with a given time point were combined to form time point service areas [B]. The dark

gray areas represent the intersection area of a time point buffer (the stop associated

with a time point) and the subsequent stop buffer. The common area was split using

the center of each horizontal street segment in the overlap area as a guide to form the

boundary between time point service areas.

3.7 GIS Allocation

A number of different methods exist for allocating socioeconomic and land use

information to transit service areas. The choice of allocation method is important

because of the potential for introducing measurement error. A study by Peng and

62

Dueker (1995) compared results from four different allocation methods (all-or-

nothing, uniform density, land use, and census block centroids) and found

considerable variation in allocated population values, depending upon the particular

method used and the level of aggregation of the source data (tract, block group, or

block). As a general rule, the lower the level of aggregation, the lower the amount of

error that will be introduced in the allocation process. Another source of measurement

error concerns competing route effects. Each transit route has an associated service

area from which it draws patronage. There are many cases where the service areas of

two or more routes overlap. Routes essentially compete for passengers in the overlap

area. Unless competing route effects are addressed, the number of persons assigned to

a given route will be overstated. This analysis attempts to control for these two

sources of error through use of improved allocation techniques.

3.7.1 Limitations of the Uniform Density Method

The uniform density method is an allocation procedure that takes into account

the proportion of land area inside a buffer relative to the parent region as a whole. For

example, if a census block group contains 500 persons and 20% of the block group

area intersects a time point buffer, then 100 persons are assigned to the time point

service area. The limitation of the uniform density assumption is that it masks any

variation present in the distribution of population and activities within an area. One

way to improve upon the uniform density method is to make use of an additional

63

attribute to allocate values to transit service areas. One such method is the street

network ratio method which is based upon the ratio of total street length within a

transit service area to total street length of the parent region (O’Neill et al, 1992). This

method uses information on street length to more precisely allocate census block

group information to transit service areas. Zhao (1998) improved upon the method

developed by O’Neill et al by incorporating a measure of residential land use into the

street network ratio method. Zhao allocated population according to the ratio of street

length for both single- and multi-family land uses inside the service area buffers to

total street length.

Although the methods developed by Zhao and O'Neill et al improve upon the

uniform density method, better estimates could be obtained using disaggregate

information related to tax parcels. This is because the distribution of population is

more closely related to the characteristics of tax parcels compared to street distance.

The analysis used residential tax parcel value along with information on the number of

housing units associated with each tax parcel to allocate socioeconomic data to transit

service areas. Although building square feet might be a more logical attribute for

allocating population, the RLIS tax lot database contained an excessive number of

missing values. Information on tax parcel value, consisting of land and building

value, was used as the basis for allocating population to time point service areas.

64

3.7.2 Competing Service Areas

Transit routes do not operate independently from one another. A portion of a

transit service area for one route may overlap with the service area of another.

Persons in the overlap area can be assumed to patronize one route or the other, but not

both. Unless these competing route effects are taken into account, the number of

persons likely to frequent a given transit route is overestimated. One method for

dealing with overlapping service areas is to divide attribute values in the common area

by a factor equal to the number of routes. This method is similar to the uniform

density assumption mentioned previously. Peng (1994) defined competing routes as

parallel routes that share a common service area and serve the same destination.

Rather than eliminating the potential for over counting using an allocation technique,

Peng measured the proportion of the population in the overlap area and used it as an

endogenous variable in the demand equations. The assumption by Peng that

competing routes must serve the same destination is restrictive in that patrons can

realistically frequent any route to which they have access. For example, a particular

employment location might have access to a radial and a crosstown route. Even

though the two routes do not serve the same destination, employees may patronize

either of the routes. Since it is not possible to know where persons are traveling to a

priori, a more conservative approach would be to control for the number of routes

accessible to each location. This analysis controls for competing route effects during

the allocation process through use of an accessibility weight. An important distinction

65

between this method and that used by Peng is that competing route effects are not

limited to overlapping service areas of routes serving the same destination.

3.7.3 Improved Time Point Service Area Allocation Methods

A number of variables used in this research involved the allocation of

socioeconomic and land use information to transit service areas using a GIS. The time

point variables that are generated include employment, population over 16 years of

age, and number of zero auto-ownership households. Employment is a disaggregate

(point) measure representing the number of employees associated with non-residential

tax parcels. Population, median household income, and zero auto ownership are

aggregate (polygon) measures associated with census block groups. The following

equation was used to allocate employment data to time point service areas.

(3.1) ∑∈

=N

ijkhhhijk RTEEMPEMP )/(

EMPijk is the number employees in the time point service area, controlling for

accessibility to other routes. Values were obtained by dividing the number of

employees at each employment location (EMPh) by the number of accessible bus

routes (RTEh), then summing over all employment locations in the time point buffer.

Subscript (h) refers to tax parcel. The set of subscripts (ijk) refers to time point buffer

(i) for a given route (j) and direction (k).

66

For aggregate measures such as population and the number of zero auto

households, a different allocation procedure was required. The procedure used

information on residential tax parcel value, the number of housing units, and the

number of accessible bus routes to allocate block group population and auto

ownership values to time point service areas. The allocation procedure required two

intermediate steps. First, a weight was developed (PVALijkl) representing the

proportion of residential tax parcel value inside the time point service area relative to

the block group as a whole.

(3.2) )/( ∑∑∈∈

=N

lhh

N

ijklhhijkl VALVALPVAL

Subscript (l) refers to block group, subscript (h) refers to an individual tax parcel, and

the set of subscripts (ijkl) refers to the portion of the block group (l) located inside the

time point buffer (i) for a given route (j) and direction (k).

The next step involved the development of a weight to control for accessibility

to other bus routes.

(3.3) )(/)*( HURTEHUAVAL h

N

ijklh

N

ijklhhhijkl ∑ ∑

∈ ∈

=

AVALijkl is a weight representing the average number of bus routes accessible to

housing units located inside the time point buffer. The first part of the equation was

calculated by multiplying the number of housing units attributed to each tax parcel

(HUh) by the number of routes accessible to each tax parcel (RTEh), then summing

67

over all tax parcels inside a time point service area. This value was divided by the

summation of all housing units in the buffer. Subscript (h) refers to an individual tax

parcel and the set of subscripts (ijkl) refers to the portion of the block group (l) located

inside the time point buffer (i) for a given route (j) and direction (k).

The following equation was used to allocate population greater than 16 years of

age to time point service areas.

(3.4) )/*(∑=N

ijklijklijkllijk AVALPVALPOPPOP

Time point service area population (POPijk) was calculated by multiplying block group

population by the value weight (PVALijkl), then dividing by the accessibility weight

(AVALijkl), then summing over all block groups intersecting the time point buffer.

The equation for calculating the number of zero auto households is the same as that for

population.

For purposes of clarification, an example showing how block group population

was allocated to time point service areas is presented in Table 3.3.

Table 3.3 Allocation of Employment to Time Point Service Areas

BG BGPOP IVAL TVAL PVAL Σ[HU*RTE] Σ[HU] AVAL POP11011 970 32.7 51.6 0.63 1597 693 2.30 26611013 423 8.2 8.2 1.00 268 100 2.68 15811014 169 1.8 1.8 1.00 52 26 2.00 8512011 762 36.1 36.1 1.00 715 679 1.05 72612015 1068 25.2 47.0 0.54 581 316 1.84 313 ΣPOP = 1548

68

In the example, 5 block groups (BG) intersect the time point buffer. The amount of

population from each block group (POP) is determined by multiplying block group

population (BGPOP) by the percent value weight (PVAL) then dividing by the

average accessibility ratio (AVAL). PVAL is the ratio of tax parcel value inside the

time point buffer (IVAL) relative to the block group as a whole (TVAL). AVAL is

the average accessibility value for housing units located inside the time point buffer.

AVAL is calculated by dividing the summation of housing units inside the buffer

multiplied by the number of accessible bus routes (Σ[HU*RTE]), then dividing by the

summation of housing units inside the buffer (Σ[HU]). The summation of POP over

all block groups results in an allocated population value (ΣPOP) of 1,548 for the time

point service area.

Two additional factors that have not been explicitly addressed concern choice

riders and service frequency. Tri-Met does not coordinate headways on routes that

share common street segments. This occurs most often on routes that converge near

downtown. Persons with access to more than one bus route serving the same

destination usually board whichever bus arrives earliest in time. The allocation

methodology developed in this research controls for accessibility to other routes.

Passengers with access to more than one route serving the same destination would

likely choose the route with the higher service frequency since it would serve to lower

average wait times. The necessary information required to control for the effects of

service frequency in the allocation process is the average headway of each competing

69

route and the distance to the nearest bus stop on each route. A weight could be

developed relating service frequency on the route of interest to that of the competing

route, controlling for distance. This study did not attempt to control for this effect

because of extensive data requirements.

3.8 Chapter Summary

Database integration is necessary for analysis of bus performance and, when

integrated with socioeconomic and land use data using a GIS, analysis of passenger

demand. A number of advanced technologies are incorporated into the BDS which

allows Tri-Met to collect substantial amounts of information on bus operations. The

sample encompasses 19 weekdays of bus operations for 5 radial and 2 crosstown

routes. The data used in this research were related to a common geography

representing a time point. Time point-level variables often pertain to different spatial

characteristics including point, polygon, and cumulative since previous time point.

The effect of cumulative distance since the route origin is controlled for in the analysis

using a measure of delay variation at the previous time point. Buffering transit stops

using street network distance more closely captures the behavior of transit users

compared to Euclidean distance buffering. Different allocation procedures are

developed depending upon whether socioeconomic and land use variables are in

aggregate or disaggregate form. It is shown how information on tax parcel value and

the number of housing units can be used in the allocation process to produce more

70

robust estimates of population, employment, and zero auto-ownership households.

Controlling for route competition in the allocation process corrects for the tendency to

over count the number of persons likely to patronize a given route. Time point-level

analysis of transit service reliability and passenger demand require that data from a

number of different sources be integrated in a spatially consistent manner using GIS

and database programming techniques.

71

CHAPTER FOUR

EMPIRICAL ANALYSIS

4.1 Introduction

The empirical analysis of transit service reliability and passenger demand is

presented in this chapter. This chapter begins with a discussion of the operational

models. The operational models attempt to follow the logic of the literature review

presented in Chapter 2. Detailed descriptions of the variables used in the analysis are

given. In some cases, proxy variables were used in place of more desirable measures

due to the lack of readily available data. The results of the transit service reliability

and passenger demand models are presented, followed by a discussion of the results.

The most common problems pertaining to estimation using OLS regression are

addressed.

4.2 Operational Models

The operational models and variable descriptions are presented in the

following section. Both the passenger demand and transit service reliability models

are stratified by route typology and time period. For radial peak period models, only

the primary direction of travel is considered. Both directions of travel are included in

the radial off-peak period models and the crosstown models. The peak period transit

service reliability models are concerned with explaining variability in bus spacing,

72

whereas the off-peak period models are concerned with explaining variability in

schedule adherence. The transit patronage models seek to explain the mean number of

boarding passengers.

4.2.1 Transit Service Reliability

Different dependent variables are used in the transit service reliability models

depending upon time period. Headway delay variation is used as the dependent

variable in the peak period models and departure delay variation in the off-peak period

models. Detailed descriptions of each of the variables used in the reliability models

are given in Table 4.1.

Table 4.1 Description of Variables: Transit Service Reliability Models

Variable Description HWDV Headway delay variation (minutes) HWDPV Headway delay variation at previous time point (minutes) DDV Departure delay variation (minutes) DDPV Departure delay variation at previous time point (minutes) HWS Scheduled headway (minutes) ONV Boarding variation (actual) OFFV Alighting variation (actual) DIST Scheduled distance (hundreds feet) USTOPV Unscheduled stop variation (actual) LIFTV Lift operation variation (actual) EVNTV Non-recurring event variation (actual) NRO Non-regular operator variation (1=true) MPH Link speed variation (miles per hour) IN Inbound direction (1=true) ES East and South direction (1=true) RTE4 Route 4 dummy (1=true) RTE8 Route 8 dummy (1=true) RTE14 Route 14 dummy (1=true) RTE15 Route 15 dummy (1=true) RTE72 Route 72 dummy (1=true) RTE75 Route 75 dummy (1=true) RTE104 Route 104 dummy (1=true)

73

The formal models developed for time point-level analysis of transit service

reliability are presented in Table 4.2. The dependent variable in each model is shown

as a diamond in the table.

Table 4.2 Operational Models: Transit Service Reliability

Reliability Radial Crosstown A.M. Mid. P.M. Eve. A.M. Mid. P.M. Eve. HWDV ♦ ♦ ♦ ♦ HWDPV • • • • DDV ♦ ♦ ♦ ♦ DDPV • • • • HWS • • • • • • • • ONV • • • • • • • • OFFV • • • • • • • • DIST • • • • • • • • USTOPV • • • • • • • • LIFTV • • • • • • • • EVNTV • • • • • • • • NROV • • • • • • • • MPHV • • • • • • • • IN • • ES • • • • RTE4 • • • • RTE8 • • • • RTE14 • • • • RTE15 • • • • RTE72 • • • •

The dependent variable in the peak period transit service reliability models is

the amount of headway delay variation (HWDV) measured in minutes for a bus trip

departing a time point calculated over all days of observations. A spatially lagged

variable, the amount of headway delay variation at the previous time point (HWDPV)

is included in the models to control for existing levels of delay variation. For the off-

peak transit service reliability models, departure delay variation (DDV) and departure

delay variation at the previous time point (DDPV) are used. The signs on the

74

coefficients for the amount of delay variation at the previous time point variables are

expected to be positive. The sizes of the coefficients are expected to equal to 1.00,

suggesting that delay variation tends to remain constant when all other explanatory

variables are held at their mean values. In theory, once headway delays set in,

passenger demand should increase at upstream stops because the delay time allows

more passengers to arrive, resulting in further delays. A coefficient value greater than

1.00 would indicate that delay variation tends to propagate over the course of a route.

A coefficient value less than 1.00 indicates that delay variation tends to diminish over

the course of a route.

Mean scheduled headway (HWS) is included in the reliability equations to

control for the amount of scheduled service on delay variation. The variable refers to

the amount of scheduled service in minutes between a bus trip and its leader. Buses

operating large headway service will likely experience greater levels of delay variation

compared to buses operating more frequently. An increase in scheduled headway is

expected to be positively associated with delay variation.

Separate passenger activity variables are used in the reliability equations

because boarding and alighting profiles are likely to vary by time period of operation

and by type of route. ONV and OFFV refer to the amount of boarding and alighting

variation since the previous time point, respectively. Experience suggests that

boarding variation will have a larger adverse impact on delay variation compared to

alighting variation since passengers typically take more time to board than alight.

75

LIFTV represents the amount of lift operation variation over a time point segment.

The variable is expected to be positively associated with delay variation.

Cumulatively, boarding variation, alighting variation, and lift operation variation are

intended to pick up the effects of passenger activity on the amount of delay variation

at each time point.

A distance variable is included in the models to control for the effects of time

point complexity. DIST refers to the amount of scheduled distance since the previous

time point measured in hundreds of feet. It is expected that an increase in scheduled

distance will lead to an increase in delay variation. Two variables are included in the

models to control for the effect of driver experience and behavior on the amount of

delay variation. USTOPV is a variable measuring the amount of variation in

unscheduled stopping activity since the previous time point. It is posited that an

increase in the unscheduled stop variation will be associated with greater levels of

delay variation. Unscheduled stops represent a way for operators to kill time if buses

are running hot. An increase in the number of unscheduled stops is indicative of

service reliability problems. NROV is a trip-level variable representing non-regular

operator variation. The variable includes both part-time and extra-board operators. It

is likely that non-regular operator variation will be associated with greater levels of

delay variation. Another operator behavior variable — late departure from terminal

variation — was considered for inclusion in the reliability models but was later

dropped from the specifications. The amount of delay variation at TP 0 (the route

origin) is picked up in the delay variation at the previous time point variable at TP 1.

76

EVNTV pertains to non-recurring event variation. The variable consists of

delay events associated with passenger activity, operators, mechanical failure,

emergencies, and traffic conditions. For trips associated with delay events, a dummy

variable was assigned to each time point downstream from the event location. MPHV

is a proxy for variability for link travel speed over a time point. The variable was

calculated by subtracting dwell time from actual running time plus a penalty of 2

seconds for each actual stop (5 seconds for off-peak time periods) to compensate for

acceleration/deceleration delay prior to aggregation. An analysis by Muller and Furth

(2001) used a similar measure of vehicle speed, but did not take into account

acceleration/deceleration delay. It is posited that an increase in link speed variation

will be associated with greater levels of delay variation.

The radial off-peak period models and the crosstown models contain the

variable IN, which is a dummy variable for inbound direction of travel. The reference

case is the outbound direction. ES is a dummy variable that refers to the East and

South directions of travel on crosstown routes, with the reference case being the North

and West direction. Various route-specific dummy variables are included in the transit

service reliability models to pick up any unexplained effects on delay variability due

to route of operation. The radial reliability models include route-specific dummy

variables pertaining to Routes 4 (RTE4), 8 (RTE8), 14 (RTE14), and 15 (RTE15).

The reference case is Route 104 (RTE104). The crosstown reliability models include

a route specific dummy variable for Route 72 (RTE72). The reference case is Route

75 (RTE75).

77

4.2.2 Passenger Demand

The models developed for time point-level analysis of passenger demand are

presented in this section. Descriptions of each of the variables used in the analysis are

given in Table 4.3.

Table 4.3 Description of Variables: Passenger Demand Models

Variable Description ONX Mean boardings (actual) HWDVP Headway delay variation at previous time point (minutes) DDVP Departure delay variation at previous time point (minutes) HWS Scheduled headway (minutes) STOP Scheduled stops (actual) POPI Population > 16 years of age, inbound direction (hundreds) POPDI Downstream population > 16 years of age, inbound direction (hundreds) EMPO Employment, outbound direction (hundreds) EMPDO Downstream employment, outbound direction (hundreds) POP Population (hundreds) EMPD Downstream employment (hundreds) TC Transit center (1=true) COMPR Complimentary radial routes (actual) COMPX Complimentary crosstown routes (actual) AUTO Zero auto-ownership households (hundreds) IN Inbound direction (1=true) ES East and South direction (1=true) RTE4 Route 4 dummy (1=true) RTE8 Route 8 dummy (1=true) RTE14 Route 14 dummy (1=true) RTE15 Route 15 dummy (1=true) RTE104 Route 104 dummy (1=true) RTE72_KL Portion of Route 72 along Killingworth (1=true) RTE72_82 Portion of Route 72 along 82nd Ave. (1=true) RTE75_LM Portion of Route 75 along Lombard (1=true) RTE75_39 Portion of Route 75 along 39th Ave. (1=true)

The operational models developed for the empirical analysis of passenger

demand are presented in Table 4.4. The dependent variable — mean boardings over

all days of observations (ONX) — is shown as a diamond in each model.

78

Table 4.4 Operational Models: Passenger Demand

Demand Radial Crosstown A.M. Mid. P.M. Eve. A.M. Mid. P.M. Eve. ONX ♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦ HWS • • • • • • • • HWDVP • • • • DDVP • • • • STOP • • • • • • • • POPI • • • POPDI • • • EMPO • • • EMPDO • • • POP • • • • EMPD • • • • TC • • • • • • • • COMPX • • • • COMPR • • • • AUTO • • • • • • • • IN • • ES • • • • RTE4 • • • • RTE8 • • • • RTE14 • • • • RTE15 • • • • RTE72_82 • • • • RTE75_LM • • • • RTE75_39 • • • •

Before proceeding with a discussion of variables used in the analysis, it must

be noted that there was a problem with the number of boarding passengers assigned to

the first time point for inbound trips departing from transit centers. Because transit

centers often represent layover points prior to the start of inbound trips, passengers

typically board buses a few minutes prior to departure. The fact that passengers are

already on board buses at the time of departure has no bearing on bus performance.

The number of passengers boarding at the route origin was not considered during the

data collection phase of the study. Assigning values from the origin location to the

79

first time point would have required deviating from the spatial structure of time points

where data are logically assigned to time points beginning with the first bus stop

following the previous time point. This omission has important implications for the

demand models because a number of boardings take place at transit centers at the

beginning of inbound trips. The locations and routes which are affected include the

Gresham Transit Center (Route 4, inbound direction), Clackamas Town Center (Route

72, North and West direction), Milwaukie Transit Center (Route 75, North and West

direction), Gateway Transit Center (Route 15, inbound direction).

HWS is the amount of scheduled service provided at the time point. The

variable represents the size of the scheduled headway in minutes. Seating capacity

was not deemed to be an important issue when developing a service quantity variable

for the demand models because the study routes operate buses with similar seating

capacities. The variable is not expected to have a significant influence on demand

because observations pertain to individual bus trips. The variable is primarily

included in the models to control for the effect of scheduled headway on the amount of

delay variation. HWDVP and DDVP are the amounts of headway delay variation at

the previous time point and departure delay variation at the previous time point for

each bus trip measured in minutes, respectively. Similar to the transit service

reliability models, the bus performance variables are differentiated by peak and off-

peak service. An increase in the amount of delay variation at the previous time point

is expected to adversely affect the number of mean boardings. STOP is the number of

scheduled stops since the previous time point. Because the number of scheduled stops

80

is directly related to passenger activity, it is expected that this variable will be

positively associated with demand.

Variables related to the size of the transit market and downstream

attractiveness require special treatment in the radial models because of the effect of

direction. Each population and employment variable used in the radial demand

models is an interaction term. POPI is the amount of population greater than 16 years

of age in a time point service area in the inbound direction of travel measured in

hundreds. EMPDI is the amount of population greater that 16 years of age

downstream from the time point in the inbound direction of travel measured in

hundreds. POPI and EMPDI are used in the radial a.m. inbound demand model as

well as the off-peak period models that include both directions of travel. EMPO and

POPDO refer to the amount of employment and downstream population in the

outbound direction of travel measured in hundreds, respectively. EMP and POPDO

are used in the radial p.m. outbound demand model as well as the radial off-peak

period models that include both directions of travel. POPDO and EMPDI are used as

proxy variables for downstream attractiveness. The expected sign of the coefficient

for POPI is positive since boardings should be positively associated with population in

the inbound direction. The expected sign of the coefficient for EMPDI for models that

include the inbound direction of travel is negative. This is because downstream

employment in the inbound direction of travel should act like a proxy for distance

from downtown. Boardings should be heavier at closer in locations. The expected

sign of the coefficient for EMPO is positive since large concentrations of employment

81

should lead to higher levels of demand on radial routes in the outbound direction of

travel. POPDO is expected to have a positive impact on demand because routes that

serve large concentrations of housing in the outbound direction will likely experience

greater levels of ridership. The crosstown demand models present a more interesting

case with respect to time point population and employment and downstream

population and employment. This is because there is not as much variation in the

population and employment variables on crosstown routes compared to radial routes.

Crosstown routes lack a strong directional bias like radial routes where employment

becomes more concentrated as distance towards downtown decreases or where

residential development becomes more concentrated as distance from downtown

increases. One would therefore expect the population and employment variables to

have less of an effect on crosstown routes. Because there is not a strong directional

bias on crosstown routes, the crosstown demand models do not use population and

employment variables differentiated by direction of travel.

TC is a dummy variable for the presence of a transit center. The downtown

Transit Mall was coded as a transit center as well. It is expected that the presence of a

transit center will be associated with greater levels of passenger demand. COMPX is

the number of complimentary crosstown routes that intersect a time point segment

associated with a radial route. The variable serves as a proxy for transfer activity. It is

expected that the number of complimentary crosstown routes will have a positive

effect on demand, especially on radial routes traveling in the inbound direction. For

the crosstown demand models, COMPR is used as a proxy variable for transfer

82

activity to and from radial routes. It is posited that an increase in the number of

complimentary radial routes will lead to an increase in demand, particularly in the

p.m. peak time period when crosstown routes intersect radial routes traveling in the

outbound direction.

AUTO is a variable that represents the number of zero auto households in a

time point service area measured in hundreds. The variable is intended to proxy for

transit-dependent riders. It is posited that an increase in the number of zero auto

households will be associated with higher levels of demand. The dummy variables for

direction of travel on radial routes (IN) and crosstown routes (ES) are the same as

those used in the transit service reliability models. Similarly, the dummy variables for

route of operation in the radial demand models are the same as those used in the radial

transit service reliability models. Because demand varies considerably on each leg of

the crosstown routes, dummy variables pertaining to each specific segment are

included in the crosstown demand models. The variables pertain to the portion of

Route 72 along 82nd (RTE72_82), the portion of Route 75 along Lombard

(RTE75_LM), and the portion of Route 75 along 39th (RTE75_39). The reference

case is Route 72 along Killingsworth (RTE72_KL).

4.3 Empirical Results

4.3.1 Introduction

The results of the transit service reliability and passenger demands models are

presented in the following section. The regression models were estimated using the

83

SHAZAM econometric software package (White, 1998). An alpha level of .05 was

used for the statistical tests. T-statistics are shown in parentheses with significant

relationships shown in bold text. When interpreting the results for the radial peak

period transit service reliability models, it is important to remember the typical

boarding profile in relation to the primary direction of travel because the two time

periods exhibit strong directionality in demand. Descriptive statistics are included in

Appendix B. Because the regression coefficients are difficult to interpret when the

independent variables refer to variances, elasticities are also presented. An elasticity

measures the percentage change in the dependent variable associated with a

percentage change in an explanatory variable. A summary table of elasticities is

presented in Appendix C.

4.3.2 Results: Radial Reliability Models

The results of the radial transit service reliability models are presented in Table

4.5. The radial peak period models explain 50% of the variation in headway delay in

the a.m. peak inbound direction and 68% of the variation in the p.m. peak outbound

direction. The radial off-peak period models explain 80% and 82% of the variation in

departure delay for the midday and evening time periods, respectively. The mean

values of the dependent variables in the radial transit service reliability models are

7.07-minutes headway delay variation in the a.m. peak, 9.33-minutes departure delay

84

variation in the midday time period, 21.70-minutes headway delay variation in the

p.m. peak, and 8.81-minutes departure delay variation in the evening time period.

Table 4.5 Results: Radial Transit Service Reliability Models

AM (IN) MID (BOTH) PM (OUT) EVE (BOTH)

D.V.

HWDV DDV HWDV DDV

HWS 0.268 (4.036)

0.098 (2.431)

0.688 (6.211)

0.011 (0.301)

HWDPV 0.750 (17.850)

--

0.957 (25.640)

--

DDPV --

0.943 (66.090)

--

0.928 (47.750)

ONV 0.033 (3.367)

0.016 (2.695)

-0.006 (-0.491)

-0.022 (-2.340)

OFFV 0.028 (3.726)

0.038 (5.766)

0.024 (1.437)

0.039 (3.279)

DIST -0.029 (-2.430)

0.010 (1.657)

0.076 (4.228)

-0.008 (-1.227)

USTOPV 0.876 (1.990)

0.589 (2.718)

0.079 (0.132)

0.248 (0.960)

LIFTV 3.475 (1.550)

4.768 (4.233)

-5.172 (-2.047)

7.638 (6.583)

EVNTV 27.529 (4.547)

9.041 (3.515)

5.887 (1.125)

4.648 (1.645)

NROV 4.191 (1.788)

-0.449 (-0.328)

1.356 (0.329)

-0.526 (-0.417)

MPHV 0.000 (-0.002)

0.040 (3.968)

0.057 (2.694)

0.022 (2.015)

IN -- -1.016 (-3.505)

--

-0.732 (-2.410)

RTE4 -1.098 (-1.264)

0.380 (0.876)

2.772 (2.004)

0.550 (1.267)

RTE8 -0.514 (-0.503)

1.475 (2.981)

4.318 (2.709)

0.417 (0.826)

RTE14 0.897 (1.176)

2.279 (4.936)

4.285 (3.059)

1.423 (3.097)

RTE15 -0.354 (-0.468)

1.679 (3.683)

3.198 (2.368)

(0.700) (1.571)

CONST 0.106 (0.076)

-2.816 (-3.273)

-12.380 (-6.200)

1.261 (1.441)

ADJ R2

0.496 0.797 0.681

0.816

N

550 1630 558 726

α=0.05, t-statistics shown in parentheses, significant variables shown in bold

85

Mean scheduled headway (HWS) is shown to have significant and positive

impact on the amount of delay variation in all time periods except for the evening time

period. The size of the p.m. peak period model coefficient for HWS indicates that a

one-minute increase in the mean scheduled headway leads to a 0.69-minute increase in

headway delay variation. The coefficients for HWS in the a.m. peak and midday time

periods show that a one-minute increase in scheduled headway results in a 0.27- and

0.10-minute increase headway delay variation and departure delay variation,

respectively. The elasticities show that a percent increase in mean scheduled headway

leads to a 0.35% increase in the amount of headway delay variability in the a.m. peak

time period and 0.31% increase in headway delay variability in the p.m. peak time

period. In the midday time period, a percent increase in mean scheduled headway is

associated with a 0.15% increase in departure delay variability.

Headway delay variation at the previous time point (HWDPV) and departure

delay variation at the previous time point (DDPV) are used in the models to control for

existing levels of delay. The variables are significant and positive across all models.

For the radial peak period models, the sizes of the coefficients for headway delay

variation at the previous time point are 0.75-minute headway delay variation and 0.96-

minute headway delay variation for the a.m. peak inbound and p.m. peak outbound

models, respectively. For the radial off-peak period models, the sizes of the

coefficients for departure delay variation at the previous time point are 0.94-minute

departure delay variation in the midday time period and 0.93-minute departure delay

variation in the evening time period. Because the values of the coefficients for the

86

amount of delay variation at the previous time point are less than 1.00, buses appear to

be experiencing diminishing delay variation over the course of a route. Hypothesis

tests on the coefficients for delay variation at the previous time point show that one

can reject the null hypotheses that the regression coefficients are equal to 1.00 in each

of the radial models, except for the p.m. peak outbound model at the 95% level of

confidence using a two-tailed t-test. The elasticity for headway delay variation at the

previous time point in the a.m. peak inbound direction model suggests that a percent

increase in the amount of headway delay variation at the previous time point leads to a

0.60% increase in headway delay variation at a time point. In the p.m. peak time

period, the elasticity for headway delay variation at the previous time point is 0.79%.

For the off-peak period models, a percent increase in the amount of departure delay

variation at the previous time point is associated with a 0.77% and 0.78% increase in

departure delay variation at a time point in the midday and evening time periods,

respectively.

The radial transit service reliability models show that variability in passenger

activity contributes to unreliable service. Boarding variation (ONV) was found to be

positively associated with headway delay variation in the a.m. peak inbound model

and departure delay variation in the midday model. Boarding variation was found to

be negatively associated with departure delay variation in the evening model. The

negative sign on the coefficient in the evening model was not anticipated. The

coefficient for boarding variation in the a.m. inbound model indicates that a one-unit

increase in the amount of boarding variation leads to a 0.03-minute increase headway

87

delay variation. The elasticity for boarding variation in the a.m. peak inbound model

suggests that a percent increase in boarding variation leads to a 0.09% increase in the

amount of headway delay variation. The elasticity for boarding variation in the

midday model indicates that a percent increase in boarding variation is associated with

a 0.03% increase in departure delay variation. The reason why boarding variation did

not prove significant in the p.m. peak outbound model is largely due to the number of

passenger boardings in relation to the spatial location of time points. The majority of

boardings on radial routes in the p.m. peak occur downtown which is also the location

of the first time point. Passenger demand is greatest at precisely the locations where

the amount of delay is likely to be least. Alighting variation (OFFV) was found to be

a significant determinant of delay variation in all models except for the p.m. peak

outbound model. The signs on coefficients for alighting variation are positive,

suggesting that an increase in the variability of alightings leads to an increase in delay

variation at time points. The elasticity for alighting variation show that a percent

increase in alighting variation leads to a 0.07% increase in the amount of delay

variation at time points for trips operating in both the a.m. peak and midday time

periods. The elasticity for the evening time period is 0.05%. Contrary to

expectations, alighting variation was not found to be a significant determinant of

headway delay variation in the radial p.m. peak outbound model. The results for the

p.m. peak outbound model show that neither boarding nor alighting variation are

significant determinants of headway delay variation in the time period. Another

passenger activity variable — variability in the number of lift operations (LIFTV) —

88

was shown to have a significant and positive effect on the amount of delay variation in

off-peak time periods. The results show that a one-unit increase in lift operation

variability contributes to 4.77-minutes departure delay variation in the midday time

period and 7.64-minutes departure delay variation in the evening time period. In the

p.m. peak outbound model, lift operation variability was found to be negatively

associated with headway delay variability. The sign on the coefficient for lift

operation variability in the p.m. peak outbound model was unexpected. A percent

increase in lift operation variability is associated with a 0.01% increase in headway

delay variability in the a.m. peak and a 0.01% decrease in the p.m. peak time period.

In off-peak time periods, a percent reduction in lift operation variability is associated

with a 0.04% reduction in departure delay variability in the midday time period and a

0.02% reduction in the evening time period. Judging by the size of the elasticities,

variability in lift operations does not appear to be a major contributor to delay

variation at time points for bus trips on radial routes. Of the three passenger activity

variables, alighting variation has the largest negative impact on the amount of delay

variation at time points.

Scheduled distance (DIST) was found to have a positive effect on headway

delay variation in the p.m. peak outbound model. For every 100-foot increase in

scheduled distance, headway delay variation was found to increase by 0.08 minutes.

The elasticity for scheduled distance in the p.m. peak outbound models is 0.29%.

Distance was found to have an unexpected negative effect on headway delay variation

in the radial a.m. peak inbound model, implying that as distance increases, headway

89

regularity actually improves. The elasticity shows that a percent increase in scheduled

distance leads to a 0.32% reduction in the amount of headway delay variation at a time

point in the radial a.m. peak model. Inspection of the data shows that the majority of

time points characterized by longer distances are located at early points along a route

where delay variation tends to be lower. The impact of scheduled distance on the

amount of delay variation in the p.m. peak is considerable given that the average

distance between time points on radial routes is approximately 8,000 feet. Since the

effects of distance are cumulative, the variable confirms expectations that delay

variation increases as distance along the route increases.

The two variables included in the models to control for operator experience

and behavior are variability in the number of unscheduled stops (USTOPV) and

variability in non-regular operator (NROV). Unscheduled stop variation was found to

be significant and positive in the a.m. and midday time periods. A one-unit increase in

the unscheduled stop variation was found to increase headway delay variation by 0.88

minutes in the a.m. peak time period and increase departure delay variation by 0.59

minutes in the midday time period. The elasticities for unscheduled stop variation

show that a percent increase in unscheduled stop variation is associated with a 0.07%

increase in the amount of headway delay variation in the a.m. peak time period and a

0.04% increase in the amount of departure delay variation in the midday time period.

Variability in non-regular operator (NROV) was not found to be a significant

determinant of headway delay variation in any of the radial models. This might

possibly be due to extra board operators being inadvertently categorized as non-

90

regular operators during the data integration phase of the study. It turns out that extra

board operators often have a considerable amount of experience and may be quite

adept at operating different routes during the course of a sign up.

Variability in delay-causing events (EVNTV) was found to have a significant

and positive effect on delay in the a.m. peak and midday time periods. The results

show that delay-causing events are associated with an increase in headway delay

variation of 27.53 minutes in the a.m. peak inbound model and an increase in

departure delay variation of 9.04 minutes in the midday model. The elasticities for

non-recurring event variation suggest a 0.07% increase in headway delay variation in

the a.m. peak time period and 0.03% increase in departure delay variation in the

midday time period. Interestingly, variability in delay-causing events was not found

to be an important determinant of headway delay variation in the p.m. peak time

period. This may possibly be due to the fact that the system is already in a state of

instability. The elasticities for non-recurring event variation are relatively low

compared to other variables used in the models.

Variability in link travel speed (MPHV) was found to be positively associated

with departure delay variation in the off-peak period models and headway delay

variation in the p.m. peak period model. A one mile-per-hour increase in link travel

speed variation results in an increase in departure delay variation of 0.04 minutes in

the midday time period and 0.02 minutes in the evening time period. The coefficient

for MPHV in the p.m. peak time period is 0.05 minutes. A percent increase in link

91

speed variability is associated with a 0.03% increase in of the amount of departure

delay variation in the midday time period, a 0.02% increase in the amount of headway

delay variability in the p.m. peak time period, and a 0.02% of the amount of departure

delay variability in the evening time period.

The off-peak period radial transit service reliability models include a dummy

variable for inbound direction of travel (IN). The variable is significant and negative

in both models. The signs on both coefficients run contrary to expectations. The size

of the coefficient in the midday model indicates a 1.02-minute improvement in

departure delay variation for bus trips operating in the inbound direction. The

coefficient in the evening time period suggests an improvement in departure delay

variation of 0.73 minutes. The unanticipated signs on the coefficients could be due to

the fact that operators sometimes take breaks prior to the end of trips when buses are

empty. This has the effect of contributing to delay variation at the last time point in

the outbound direction of travel.

Various route dummies are included in the radial transit service reliability

models to control for any unexplained effects due to route of operation. The reference

case in each model is Route 104 (RTE104) which connects Gresham with downtown

Portland. Not one route dummy variable proved significant in the a.m. peak inbound

model. The dummy variables for route of operation in the midday models were all

significant and positive with the exception of Route 4 (RTE4) which did not prove

significant. Route 8 (RTE8) is associated with an increase of 1.48-minutes departure

92

delay variation in the midday time period. Route 14 (RTE14) and Route 15 (RTE15)

are associated with increases in departure delay variation of approximately 2.28 and

1.68 minutes, respectively. The values for the route dummy variables for the pm. peak

outbound models are all significant and positive. The coefficient values range from a

low of 2.77-minutes delay variation for Route 4 to 4.32-minutes delay variation for

Route 8. Route 14 was the only route found to be associated with an increase in delay

variation in the evening time period. Route of operation appears to be an important

predictor of delay variation primarily in the midday and p.m. peak time periods.

4.3.3 Results: Crosstown Reliability Models

The results of the crosstown transit service reliability models are presented in

Table 4.6. The crosstown models differ from the radial models in that the peak period

models include both directions of travel. The crosstown peak period models explain

76% of the variation in headway delay in the a.m. peak time period and 74% of the

variation in the p.m. peak. The off-peak period models explain 84% and 92% of the

variation in departure delay for the midday and evening time periods, respectively.

The mean values of the dependent variables in the crosstown transit service reliability

models are 12.02-minutes headway delay variation in the a.m. peak, 6.53 minutes

departure delay variation in the midday time period, 20.49 minutes headway delay

variation in the p.m. peak, and 9.00-minutes departure delay variation in the evening

time period.

93

Mean scheduled headway (HWS) is shown to have significant impact on delay

variation in all time periods except for the evening time period. The signs of the

coefficients are positive, meaning that an increase in scheduled headway results in

increased levels of delay variation. The largest coefficient is associated with the p.m.

peak time period where a one-minute increase in scheduled headway results in a 0.95-

minute increase in headway delay variation. Similar to the radial transit service

reliability models, mean scheduled headway is an important determinant of delay

variation on crosstown routes. The elasticities show that a percent increase in mean

scheduled headway leads to a 0.32% increase in the amount of headway delay

variation in the a.m. peak time period, a 0.16% increase in the amount of departure

delay variation in the midday time period, and a 0.45% increase in the amount of delay

variation in the p.m. peak time period. Similar to the radial transit service reliability

models, service characteristics are found to be an important determinant of delay

variation at the time point level of analysis.

94

Table 4.6 Results: Crosstown Transit Service Reliability Models

AM (BOTH) MID (BOTH) PM (BOTH) EVE (BOTH)

D.V.

HWDV DDV HWDV DDV

HWS 0.329 (3.911)

0.089 (2.389)

0.968 (8.578)

-0.029 (-0.382)

HWDPV 0.991 (35.100)

--

0.948 (31.920)

--

DDPV --

0.988 (58.720)

--

1.054 (58.020)

ONV 0.019 (1.927)

0.000 (-0.167)

0.009 (0.653)

0.027 (2.752)

OFFV 0.024 (3.445)

0.014 (3.623)

0.038 (2.106)

0.050 (4.810)

DIST 0.023 (3.301)

0.003 (1.344)

0.030 (2.849)

0.007 (1.943)

USTOPV -0.550 (-1.263)

0.268 (1.794)

0.732 (1.092)

0.080 (0.284)

LIFTV 2.841 (0.876)

3.350 (4.963)

2.486 (0.620)

1.768 (1.197)

EVNTV 4.800 (1.200)

7.780 (4.635)

6.129 (1.192)

5.580 (2.638)

NROV -1.583 (-0.708)

0.092 (0.117)

8.076 (2.233)

2.938 (2.194)

MPHV 0.155 (4.823)

0.004 (0.755)

0.055 (2.178)

-0.001 (-0.323)

ES -1.032 (-2.143)

-0.312 (-2.000)

-0.944 (-1.340)

0.083 (0.351)

RTE72 1.389 (2.560)

-0.173 (-0.746)

1.002 (1.132)

-0.762 (-2.456)

CONST -5.397 (-3.863)

-0.585 (-0.932)

-10.714 (-5.520)

-0.413 (-0.336)

ADJ R2

0.760 0.836 0.736 0.918

N

605 1195 685 487


Headway delay variation at the previous time point (HWDPV) and departure

delay variation at the previous time point (DDPV) are found to be significant and

positive in all time periods. The values of the coefficients for headway delay

variability at the previous time point are 0.99-minute delay variation in the a.m. peak

95

time period and 0.95-minute delay variation in the p.m. peak. The values of the

coefficients for departure delay variability at the previous time point are 0.99-minute

delay variation in the midday time period and 1.05-minutes delay variation in the

evening time period. Hypothesis tests on the coefficients for delay variation at the

previous time point show that one cannot reject the null hypotheses that the regression

coefficients are equal to 1.00 in any of the crosstown reliability models except for the

evening model at the 95% level of confidence using a two-tailed t-test. This is in

contrast to the radial reliability models where only the p.m. peak outbound model

showed that the value of the headway delay variation at the previous time point

coefficient had a statistically significant probability of being equal to 1.00. The

elasticities for headway delay variability at the previous time point in the a.m. peak

and p.m. peak time periods are 0.80% and 0.78%, respectively. The elasticities for

departure delay variability at the previous time point in the midday and evening time

periods are 0.79% and 0.89%, respectively.

The coefficient for the amount of boarding variation (ONV) at time points on

crosstown trips is significant and positive in the evening time period only. The

elasticity for boarding variation is 0.04% in the time period. The variable just missed

the cutoff at the 95% level of confidence in the a.m. peak time period. Similar to the

p.m. peak radial outbound model, boarding variation was not found to be a significant

determinant of unreliable bus service on crosstown routes operating in the p.m. peak

time period. Alighting variation (OFFV) was found to be a significant determinant of

delay variation in all time periods. The coefficient values are 0.02 minutes in the a.m.

96

peak time period and 0.04 minutes in the p.m. peak time period. The off-peak period

coefficients for alighting variation are 0.01 minutes and 0.05 minutes for the midday

and evening time periods, respectively. The elasticities for alighting variation are

0.04% in the a.m. peak, midday, and p.m. peak time periods. The elasticity for

alighting variation for the evening time period is 0.07%. Lift operation variation

(LIFTV) was found to be a significant contributor to delay on crosstown routes in the

midday time period only. The elasticity for lift operation variation in the midday

model is 0.02%. The findings for lift operation variation contrast with the radial

models where lift operation variability was found to be a significant determinant of

delay variability in 3 out of the 4 models.

The variable for time point characteristics (DIST) was found to be positively

associated with delay variation in the peak period models. The variable just missed

the 95% level of confidence in the evening model. The peak period models are

associated with a 0.02- and 0.01-minute increase in headway delay variation per 100-

foot increase in scheduled distance for the a.m. peak and p.m. peak time periods,

respectively. The elasticities for scheduled distance are 0.19% in the a.m. peak time

period and 0.15% in the p.m. peak time period. The results of both the radial and

crosstown transit service reliability models show that scheduled distance is an

important determinant of delay variability for bus trips operating during peak time

periods.

97

Variability in delay-causing events (EVNTV) was found to be positively

associated with the amount of departure delay variation in the off-peak period

crosstown transit service reliability models. A one-unit increase in event variation

results in an increase in departure delay variation of 7.78 minutes in the midday time

period and 5.58 minutes in the evening time period. The elasticity values indicate that

a percent increase in delay-causing event variation is associated with a 0.03% increase

in departure delay variation in the midday time period and 0.02 increase in the evening

time period. Non-regular operator variation (NROV) was found to be an important

determinant of delay variation in the p.m. peak and evening time periods. A one-unit

increase in non-regular operator variation is associated with an increase of 8.08-

minutes headway delay variation in the pm. peak model and 2.94-minutes departure

delay variation in the evening model. The elasticities for variability in non-regular

operators is associated with a 0.04% increase in headway delay variation in the p.m.

peak time period and a 0.03% increase in departure delay variation in the evening time

period. The proxy variable for link travel speed (MPHV) was found to be significant

and positive in the peak period models. A one-unit increase in MPHV is associated

with a 0.15-minute increase in headway delay variation in the a.m. peak time period

and a 0.06-minute increase in the p.m. peak time period. The elasticities for MPHV in

the two time periods are 0.08% and 0.02%, respectively.

The dummy variables for travel in the East/South direction (ES) were found to

be significant and negative in the a.m. peak and midday time periods. Bus trips

operating in the East/South direction experience 1.03 minutes less headway delay

98

variation over time points in the a.m. peak time period, and 0.17 minutes less

departure delay variation in the midday time period. The dummy variables for Route

72 (RTE72) were shown to be associated with greater levels of headway delay

variation in the a.m. peak time period and lower levels of departure delay variation in

the evening time period, compared to Route 75 (RTE75).

4.3.4 Results: Radial Demand Models

The radial transit patronage models seek to explain the number of mean

boardings over a time point segment. Observations refer to individual bus trips at time

points averaged over all days of observations. The results of the radial demand

models are presented in Table 4.7. The models explain 75% of the variation in mean

boardings in the a.m. peak and p.m. peak time periods. The models explain 60% of

the variation in mean boardings in the midday and evening time periods. The mean

values of the dependent variables in the radial passenger demand models are 8.81

boardings in the a.m. peak time period, 6.46 boardings in the midday time period, and

8.32 and 4.60 boardings in the p.m. peak and evening time periods, respectively.

Mean scheduled headway was not found to be a significant determinant of

demand in any of the radial demand models. The hypothesis tests for HWS in the a.m.

peak, p.m. peak, and evening time periods just missed the cutoff point at the 95% level

of confidence. This finding is somewhat expected given that observations refer to

individual trips. Neither the amount of headway delay variation at the previous time

99

point (HWDVP) nor the amount of departure delay variation at the previous time point

(DDVP) were found to be significant in any of the time periods.

Table 4.7 Results: Radial Passenger Demand Models

AM (IN) MID (BOTH) PM (OUT) EVE (BOTH)

D.V.

ONX ONX ONX ONX

HWS 0.076 (1.848)

0.027 (0.981)

0.110 (1.788)

-0.071 (-1.878)

HWDVP -0.006 (-0.206)

--

-0.001 (-0.052)

--

DDVP --

0.007 (0.764)

--

0.021 (1.053)

STOP 0.013 (0.226)

0.149 (4.381)

0.122 (1.333)

0.060 (1.138)

POPI 0.395 (9.287)

0.236 (16.100)

--

0.181 (8.110)

EMPDI -0.053 (-6.600)

-0.018 (-3.220)

--

0.029 (3.381)

EMPO --

0.192 (15.810)

0.372 (13.700)

0.228 (12.640)

POPDO --

0.051 (11.610)

0.073 (6.660)

0.051 (7.825)

TC 1.729 (2.810)

2.416 (8.683)

7.136 (9.619)

3.431 (8.156)

COMPX 1.619 (6.257)

1.247 (7.461)

1.442 (2.513)

0.360 (1.434)

AUTO 1.226 (3.794)

0.372 (3.298)

0.090 (0.366)

-0.222 (-1.298)

IN --

3.429 (7.887)

--

0.543 (0.835)

RTE4 -0.263 (-0.413)

2.520 (7.959)

7.502 (9.079)

4.073 (8.683)

RTE8 1.135 (1.680)

0.951 (2.664)

5.393 (5.980)

3.398 (6.329)

RTE14

2.235 (4.534)

3.048 (9.047)

6.813 (7.341)

4.451 (8.855)

RTE15 1.272 (2.490)

0.272 (0.762)

0.013 (0.013)

0.621 (1.185)

CONST -1.179 (-1.325)

-5.451 (-7.631)

-10.727 (-7.042)

-4.136 (-3.905)

ADJ R2

0.752

0.601

0.745

0.603

N

550 1630

558 726


100

This finding suggests that the amount of delay variation at the previous time point has

no effect on passenger demand on trips associated with radial routes at the time point

level of analysis. The number of scheduled stops (STOP) was found to be an

important determinant of mean passenger boardings in the midday time period only.

The sign on the coefficient for scheduled stops is positive, indicating that an increase

of one scheduled stop results in an increase in passenger demand of 0.15 boardings per

trip, per time point.

The market size and downstream attractiveness variables are all significant and

have the expected signs on the coefficients. The radial a.m. peak inbound model

indicates that an increase in time point population (POPI) of 100 persons results in an

increase in demand of 0.40 persons. The coefficient value for downstream

employment (EMPDI) in the time period is -0.05 boardings per 100-person increase in

downstream employment. The negative sign on the coefficient for EMPDI is expected

given that more persons are likely to board at close-in time points compared to those

further away. The coefficients for POPI and EMPDI in the midday model are similar,

except that the sizes of the coefficients are smaller. The coefficient for time point

employment in the outbound direction of travel (EMPO) in the midday time period

indicates 0.19 boardings per 100-person increase in employment. The coefficient for

downstream population in the outbound direction of travel (POPDO) shows 0.51

boardings per 100-person increase in downstream population. The p.m. peak

outbound model has the largest coefficient for time point employment at 0.37 boarding

passengers per 100-person increase in employment. The coefficient of downstream

101

population is also largest in the p.m. peak outbound model. The coefficients for the

evening model are similar to the midday model with the exception of the inbound

downstream employment variable which has a positive sign in the evening time

period. Since downtown serves as an attractive entertainment destination, the positive

sign in the evening time period seems reasonable.

The dummy variable for transit center (TC) proves significant in all time

periods. The presence of a transit center in the a.m. peak time period is associated

with an increase of 1.73 boardings per trip and 7.12 boardings per trip in the p.m. peak

time period. The coefficients for off-peak models are 2.42 passengers in the midday

time period and 3.43 passengers in the evening time period. The estimated coefficient

for TC is likely to be underestimated in all models except for the p.m. peak outbound

model, given the data collection problems mentioned previously where information on

the number of boardings occurring at outlying transit centers at the beginning of

inbound trips was not collected. An additional source of originating riders concerns

passengers who transfer from other routes. The proxy variable for transferring

passengers (COMPX) is significant and positive in all models except for the evening

time period model. An increase in the number of complimentary radial routes is

associated with an increase in demand of 1.62 passengers in the a.m. peak inbound

model, 1.25 passengers in the midday model, and 1.44 passengers in the p.m. peak

outbound model. The largest coefficient is associated with the a.m. peak inbound

model. This is consistent with expectations, given that radial routes attract boarding

passengers from crosstown routes in the inbound direction of travel, whereas in the

102

outbound direction of travel, fewer people transfer from crosstown routes to radial

routes.

The variable for the number of zero auto households (AUTO) attributed to a

time point service area is significant and positive in the a.m. peak and midday models.

The largest effect of an increase in the number of zero auto households is associated

with the a.m. peak model where an increase of 100 households with zero automobiles

leads to an increase in the number of mean boardings by 1.23 passengers per trip, per

time point. One would expect the size of the coefficient for AUTO to be larger in off-

peak time periods since the proportion of captive riders is greater. This expectation is

not confirmed by the results of the radial demand models. The insignificance of the

variable for AUTO in the p.m. peak seems reasonable given that journey from work

trips dominate in the time period. The dummy variable for inbound direction of travel

(IN) is significant and positive in the midday model only with inbound travel

associated with an increase in mean boardings of 3.43 passengers.

The route dummy variables capture any unexplained effects in the models due

to route of operation. The dummy variables for Route 14 (RTE14) and Route 15

(RTE15) are shown to be significant determinants of ridership in the a.m. peak time

period. The effect of Route 14 on mean boardings in the a.m. peak time period is 2.24

passengers per trip compared to Route 104 (RTE104), the reference case. The effect

of Route 15 on mean boardings in the a.m. peak time period is 1.27 passengers per

trip. The midday models show a significant increase in ridership of 2.52 boardings for

103

Route 4, 0.95 boardings for Route 8 (RTE8), and 3.05 boardings for Route 14. Route

4 is associated with an increase in boardings of 7.50 passengers per trip in the p.m.

peak time period. Route 8 and Route 14 are associated with an increase in boardings

in the p.m. peak of 5.39 and 6.81 passengers, respectively. Route 14 is the only route

that is significantly different from Route 104 in all 4 time periods. Route 14 also has

the largest coefficients of any of the routes in each time period with the exception of

Route 4 in the p.m. peak time period.

4.3.5 Results: Crosstown Demand Models

The crosstown transit patronage models seek to explain the number of mean

boardings over time point segments for individual bus trips. The results of the

crosstown demand models are presented in Table 4.8. The crosstown demand models

do not perform nearly as well as the radial demand models. A large part of the reason

for this has to do with the fact that there is not as much variability in mean boardings

over time points on trips associated with crosstown routes compared to radial routes.

The models explain 26% of the variation in demand in the midday time period, with a

high of 48% of the variation in demand explained in the evening time period. For the

a.m. peak and p.m. peak time periods, the models explain 40% and 33% of the

variation in mean boardings, respectively.

The size of the scheduled headway (HWS) has no significant effect on the

number of mean boardings except in the midday time period where a one-minute

104

increase in scheduled headway is associated with a decrease in demand of 0.18 mean

boardings. The relevance of this finding is limited given that observations refer to

individual trips. The variable might simply be picking up the effects of a short line

pattern change that takes place on the outer portion of Route 72 along Killingsworth.

Table 4.8 Results: Crosstown Passenger Demand Models

AM (BOTH) MID (BOTH) PM (BOTH) EVE (BOTH)

D.V.

ONX ONX ONX ONX

HWS

0.019 (0.322)

-0.188 (-2.990)

0.063 (1.103)

-0.144 (-1.868)

HWDVP 0.007 (0.319)

--

-0.033 (-1.914)

--

DDVP

--

0.062 (2.254)

--

0.026 (1.437)

STOP

-0.036 (-0.412)

0.095 (1.320)

-0.088 (-0.950)

0.099 (2.327)

POP 0.114 (2.265)

-0.051 (-1.240)

0.062 (1.167)

-0.068 (-2.342)

EMPD

0.089 (11.250)

0.074 (12.520)

0.086 (10.340)

0.083 (15.230)

TC 0.112 (0.165)

-1.788 (-3.294)

0.743 (1.056)

0.180 (0.429)

COMPR -0.175 (-1.124)

0.223 (1.789)

0.096 (0.589)

0.286 (2.504)

AUTO 3.942 (6.240)

3.559 (7.015)

3.937 (5.999)

2.775 (6.099)

ES -1.018 (-2.933)

-0.012 (-0.044)

-0.076 (-0.211)

-0.672 (-2.658)

R72_82

5.522 (8.285)

6.742 (13.150)

5.374 (8.029)

5.007 (10.460)

R75_LM

4.899 (6.424)

5.725 (8.959)

5.425 (7.005)

2.827 (5.710)

R75_39

3.000 (4.095)

6.296 (10.370)

4.547 (6.190)

2.866 (5.528)

CONST -5.540 (-4.161)

-3.261 (-3.109)

-4.478 (-3.784)

-3.168 (-2.562)

ADJ R2

0.400

0.259

0.330

0.479

N

605

1195

685

487


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The amount of headway delay variation at the previous time point (HWDVP) has no

statistically significant effect on demand on crosstown routes in either of the peak time

periods. The variable just missed the cutoff point at the 95% level of confidence in the

p.m. peak time period.

The amount of departure delay at the previous time point (DDVP) is

significant and positive in the midday model. The positive sign on the coefficient is

unexpected. It was expected that an increase in departure delay variation would have

a negative impact on demand. One possible explanation for the positive sign on the

coefficient is that midday demand on crosstown routes tends to be higher at locations

where service reliability is poorer. The elasticity shows that a percent increase in the

amount of departure delay variation at the previous time point leads to a 0.04%

increase in mean boardings over a time point. The headway delay variation at the

previous time point variable in the pm. peak model was also close to being statistically

significant, with a negative sign on the coefficient.

Time point population (POP) was found to be significant and positive in the

a.m. peak time period. The size of the coefficient indicates that an increase in time

point population of 100 persons results in a 0.11 increase in the number of mean

boardings. The variable for time point population proved significant and negative in

the evening time period. The proxy for destination attractiveness — downstream

employment (EMPD) — was found to be significant and positive in all time periods.

The coefficients range from a low of 0.07 boardings per trip to a high of 0.09

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boardings. The usefulness of this variable as a predictor of demand is somewhat

limited given that few persons travel from one end of a crosstown route to the other.

The number of scheduled stops (STOP) was found to be an important

determinant of mean boardings over a time point in the evening time period only. The

size of the coefficient indicates that an increase in one scheduled stop leads to an

increase in demand of 0.10 boardings per trip, per time point in the time period. The

number of complimentary radial routes (COMPR) proved significant in the evening

model only. An increase in one complimentary radial route is associated with an

increase of 0.29 boardings in the evening model. It was expected that the variable

would prove significant and positive in the p.m. peak time period since there are a

considerable number of boarding passengers originating from radial routes traveling in

the outbound direction. The dummy variable for the presence of a transit center in a

time point (TC) was not found to be an important determinant of passenger demand on

crosstown routes. TC is significant and has an unexpected negative sign in the midday

model.

The number of zero auto households (AUTO) has a significant and positive

effect on mean boardings in all time periods. The coefficients range from a low of

2.78 passengers for a 100-household increase in the number of zero auto households in

the evening time period to a high of 3.94 passengers in the a.m. peak and midday time

periods. These results suggest that auto ownership has a major effect on demand on

crosstown routes and that the effect is greater than that found in the radial models.

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The dummy variable for direction (ES) is found to be significant and negative in the

a.m. peak and evening time periods. The East and South direction of travel is

associated with a decrease in mean boardings of 1.02 persons per trip, per time point

in the a.m. peak, and 0.67 persons in the evening time period compared to the North

and South direction. Demand in the midday and p.m. peak time periods does not

appear to be directionally biased.

Since demand on the two crosstown routes is largely a function of the

particular route segment of operation, dummy variables pertaining to the individual

route segment of operation were assigned to time points. The reference case is Route

72-Killingsworth (RTE72_KL). The dummy variable for the time points located on

Route 72 along 82nd (RTE72_82) is significant and positive in all time periods. The

route segment is associated with an increase in mean boardings ranging from a low of

5.01 boardings in the evening time period to a high of 6.74 boardings in the midday

time period. The dummy variable for Route 75-Lombard (RTE75_LM) performs

similarly except that the smallest coefficient is associated with the evening time

period. The route segment pertaining to Route 75-39th (RTE75_39) also proves

significant and positive in all time periods. The values range from a low of 2.87

passengers in the evening time period to a high of 6.30 passengers in the midday time

period. Route 72-82nd is associated with the higher levels of mean boardings in 3 of 4

time periods which is consistent with expectations, given that it is the highest ridership

route in the Tri-Met system. The results show that the particular route segment of

operation has a large and positive effect on demand on crosstown routes.

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4.4 Modeling Issues

Because of data limitations, a number of variables in the analysis are proxies

for more desirable measures. The consequence of using a proxy variable is that the

regression coefficient is biased towards zero if it can be ascertained that the proxy

variable does not covary with any of the other independent variables. While this may

appear to be a serious problem, it actually results in a more stringent test of the

hypothesis that the regression coefficient is equal to zero. If two or more variables are

measured with error, then one cannot tell the direction of the biases. In the interests of

maintaining proper model specifications in this research, the use of proxy variables is

deemed more important than suffering the consequences of omitting relevant

variables.

OLS regression models are based upon a number of critical assumptions that

must be addressed in further detail. The most likely problems with cross-sectional

regression models pertain to specification error, multicollinearity, and

heteroskedasticity. Specification error can take many forms including omitted

variables, the inclusion of irrelevant variables, and incorrect functional form. There

are no prior theoretical reasons for believing that the expected relationships between

each of the independent variables and the dependent variables are non-linear. Scatter

diagrams of a number of independent variables against each dependent variable

showed the relationships to be either linear in nature or of no discernable pattern. The

operational models match as closely as possible with existing theory given limitations

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on data availability. In many cases, the data underwent extensive processing in a GIS

or database program in order to produce more desirable variables.

Heteroskedasticity is a common problem in cross-sectional models.

Heteroskedasticity refers to the problem of non-constant error variance. The

consequences of ignoring heteroskedasticity are that the standard errors of the

estimates are biased, making hypothesis tests invalid. The regression coefficients are

unbiased, but inefficient. Simple visual inspections for heteroskedasticity were

performed by plotting the standardized residuals from each regression models on the

horizontal axis against the dependent variable. Several of the residual plots indicated

the presence of heteroskedasticity. A diagnostic test was performed in SHAZAM to

formally test for the presence of heteroskedasticity. The diagnostic test rejected the

null hypothesis of homoskedasticity in every model. White's heteroskedasticity-

consistent covariance matrix correction was used to correct for unknown forms of

heteroskedasticity (White, 1980). The heteroskedasticity-corrected t-scores were

compared with the t-scores from the original (uncorrected) models. Table 4.9 presents

a summary of the variables that changed in significance between the original and

heteroskedasticity-corrected models. The table shows that 17 variables change in

significance over all 8 models following correction for heteroskedasticity, with 12

variable going from significant to insignificant, and 5 variable from insignificant to

significant. The majority of problems are associated with the transit service reliability

models. According to Crown (1998), if the estimated coefficients are statistically

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significant despite presence of heteroskedasticity, then there is little need for

correction.

Table 4.9 Heteroskedasticity: Comparison of Corrected and Uncorrected T-scores

Model Variable Time Period Original T-score Corrected T-score Reliability: Radial NROV A.M Peak 1.788 2.075 Reliability: Radial ONV Midday 2.695 1.240 Reliability: Radial OFFV Midday 5.766 1.369 Reliability: Radial USSV Midday 2.718 1.411 Reliability: Radial MPHV P.M Peak 2.694 1.209 Reliability: Radial ONV Evening -2.340 -1.706 Reliability: Radial MPHV Evening 2.015 1.074 Reliability: Radial IN Evening -2.410 -1.751 Reliability: Crosstown RTE72 A.M. Peak 2.560 1.340 Reliability: Crosstown CONST A.M. Peak -3.863 -1.172 Reliability: Crosstown ES Midday -2.000 -1.830 Reliability: Crosstown HWS P.M Peak 8.578 1.493 Reliability: Crosstown MPHV P.M Peak 2.178 0.818 Demand: Radial HWS P.M. Peak 1.788 2.553 Demand: Radial AUTO Evening -1.298 -1.999 Demand: Crosstown COMPR Midday 1.789 2.107 Demand: Crosstown HWS Evening -1.868 -1.998

However, many variables fall out of significance in the transit service reliability

models. Because there are risks associated with the improper correction for

heteroskedasticity, the models presented in this analysis represent the original,

uncorrected scores. The reader is left to decide which set of scores is more

appropriate.

Multicollinearity is often a serious problem in OLS models. If two or more

independent variables are found to be highly correlated, then it is difficult to separate

out the effects of each of the variables on the dependent variable. If multicollinearity

is present between two or more variables, then the standard errors of the regression

coefficients will be higher, resulting in lower t-statistics. The regression coefficients

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may appear insignificant when in fact they are significant. OLS estimates are still

unbiased and consistent and hypothesis tests are still valid. It is not believed that there

are problems with multicollinearity in the transit service reliability models. This is

because there is little theoretical overlap between the independent variables. Although

simple correlation coefficients are a crude way to check for the presence of

multicollinearity, only one transit service reliability model contained a pair of

variables exhibiting a correlation coefficient above an absolute value of 0.65,

suggesting few concerns. In the case of the passenger demand models, the paired

variables with correlation coefficients above an absolute value of 0.65 pertain to the

following: population (POP) and zero auto-ownership households (AUTO) in 3 of the

4 models; population (POP) and the number of scheduled stops (STOP) in the a.m.

inbound model, and the interaction variables for population (POPI and POPDO) and

employment (EMPO and EMPDO) with inbound direction of travel (IN) in the off-

peak period models. The large sample sizes of the models will likely minimize any

adverse consequences resulting from multicollinearity.

4.5 Chapter Summary

The empirical models developed for time point-level analysis of transit service

reliability and passenger demand are formally presented. The models match as closely

as possible to existing theory, taking into account the fact that the analysis uses

observations that refer to individual trips at time points. Detailed descriptions of the

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variables used in the analysis are given. The results of the transit service reliability

and passenger models are presented. With the exception of the crosstown demand

models, the results of most of the models appear reasonable. A discussion of the

findings is presented in the next chapter, along with suggestions for future

improvements, and the conclusions of the analysis.

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CHAPTER FIVE

DISCUSSION AND CONCLUSIONS

5.1 Introduction

The results of the transit service reliability and passenger demand models have

a number of implications for transit service planning, scheduling, and operations

control. The findings of the transit service reliability models also have important

implications for passengers since delay variation directly influences passenger wait

times. The analysis uses observations that refer to individual bus trips at time points

summarized over multiple days. When interpreting the parameter estimates, it is

useful to think in terms of complete trips consisting of several time points.

5.2 Applications

Since observations refer to individual trips at time points, the interpretation of

the regression coefficients in the demand models requires that one take into account

the number of time points associated with a route and the number of trips in the time

period. For example, Route 14 consists of 6 time points with 30 trips operating in the

inbound direction in the midday time period. The regression coefficient for inbound

population is 0.24 mean boardings per trip, per time point. Assuming an increase of

time point service area population of 100 persons (1 unit) in a single time point, the

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expected increase in the number of passengers for Route 14 midday time period,

inbound direction of travel is 7.24 boardings over all 30 trips in the time period.

Assuming 255 weekdays of operation per year, the increase in time point population

translates to an annual increase in demand of approximately 3,500 person trips. A

table showing the number of trips associated with each route, direction, and time-of-

day component is given in Appendix D. This type of analysis is useful for each of the

population and employment variables as well as the variable pertaining to the number

of zero auto-ownership households. It is also possible to analyze changes in the level

of a variable in more than one time point, extrapolate them to the trip level, and then to

the service period. For example, if population is expected to increase differentially

along a route due to regional land use development policies, a transit service planner

can simply plug in expected values to analyze potential ridership impacts.

The following example shows how to interpret the headway delay variation at

the previous time point, and departure delay variation at the previous time point

coefficients. The example uses departure delay variation as the variable of interest.

The initial assumption is 2.00-minutes departure delay variation at TP 1. This is

representative of a delay encountered between the route origin and the first time point.

In the first scenario (Case 1), the coefficient for departure delay variation is 0.90

minutes. If one multiplies the amount of departure delay variation at each time point

by the value of the coefficient, it can be seen that a coefficient with a value of less than

1.00 has a diminishing effect on delay. The amount of departure delay variation at the

first time point is 2.00 minutes, but decreases at a decreasing rate by the last time

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point. There appears to be enough run time built into the schedule so that the system

is essentially self-correcting. In Case 2, the coefficient value is 1.00. It can be seen

from the example that the amount of delay at the first time point remains constant

across all time points.

Departure delay at TP 1 = 2.00 minutes

Case 1: Coefficient for departure delay variation at previous time point = 0.90 minutes Case 2: Coefficient for departure delay variation at previous time point = 1.00 minutes Case 3: Coefficient for departure delay variation at previous time point = 1.10 minutes

Figure 5.1 Interpretation of Delay Variation at Previous Time Point Coefficient

T

1.2.

TP 0 P 5 TP 4 TP 3 TP 2 TP 1

2.00 1.801.62 31 1.46 2.00 2.002.00 00 2.00 2.00 2.202.42 2.93 2.66

Case 1

Case 3 Case 2

Start

In Case 3, the coefficient value for departure delay variation at the previous time point

is 1.10 minutes. This has the effect of increasing the amount of delay over time points

at an increasing rate. A coefficient value greater than 1.00 suggests that operators are

not provided enough recovery time to account for variable service conditions. This is

the worse case scenario from the perspective of both passengers and the transit agency

because once buses fall behind, then delays tend to propagate.

An important point to remember is that all other variables are held at their

mean values in the above example. The general tendency is for delay variation to

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increase as buses progress along a route. The coefficient for scheduled distance in the

a.m. peak crosstown model is 0.02-minutes delay variation per 100 feet of distance. A

crosstown bus route consisting of 10 time points spaced 1.5 miles apart would

experiences 1.58-minutes delay variation at the first time point and reach 15.80-

minutes delay variation by the last time point because the effects of distance are

cumulative. Furthermore, once buses become delayed, then passenger demand should

increase as the spacing between buses becomes greater. Using the example given in

Figure 5.1, if the amount of scheduled run time between the route origin and the first

time point is 10 minutes, then actual run time is 12 minutes (due to the 2-minute

increase in delay variation). This represents a 20% increase in run time. If the 20%

increase in run time were extrapolated to boarding and alighting variation, then the

delay effects would be much larger than those shown in the example because of the

dynamic interaction between bus delays and passenger activity.

5.3 Discussion

5.3.1 Transit Service Reliability Models

The results of the transit service reliability models show that the amount of

delay variation at the previous time point has a highly significant effect on the amount

of headway delay variation in peak time periods and departure delay variation in off-

peak time periods for both radial and crosstown routes. In all but one of models, the

size of coefficients for delay variation at the previous time point is less than 1.00.

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Individual tests preformed on the coefficients reject the null hypothesis that the

coefficients are equal to 1.00 in 3 out of 4 radial models and 1 out of 4 crosstown

models. Regardless of the test results, the values of the delay variation coefficients are

so close to 1.00 that there appears to be sufficient recovery time built into schedules.

The only comparable study was undertaken by Abkowitz and Engelstein (1983) who

analyzed run time variation at the route-segment level of analysis. The authors

included a lagged variable to control for existing levels of run time variation and

found that run time variation tends to increase as vehicles progress along a route,

though their interpretation of the size of the coefficient is subject to debate. The

results suggest that reducing delay variation at time points by using control actions

such as vehicle holding will produce benefits to passengers in the form of more

predictable service, and that any reductions will, for the most part, be proportional to

the level of the initial reduction. The other implication is that building enough running

time into schedules will allow operators to adjust vehicle speeds and stopping activity

to better maintain service reliability.

The amount of scheduled service was found to be positively associated with

delay variation in both the radial and crosstown transit service reliability models in all

time periods except for the evening time period. This finding is largely consistent

with the results of previous studies which found that delays increase with increases in

scheduled service (Abkowitz & Engelstein, 1984; Strathman & Hopper, 1993).

Another variable found to have a substantial effect on delay variation in certain

models was the amount of scheduled distance. The variable proved significant in the

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peak time period models for both radial and crosstown routes. The signs on the

distance coefficients were positive in all models except for the radial a.m. peak

inbound model. In the radial a.m. peak inbound model, distance was associated with a

reduction in headway delay variability. The finding that delays tend to increase with

distance is supported by research by Abkowitz & Engelstein (1983, 1984).

The effect of boarding and alighting variation on the amount of delay variation

at time points is inconsistent across route types and time periods of operation. In

general, alighting variation appears to have a greater effect on delay variation than

boarding variation for both radial and crosstown routes. For radial routes, variability

in passenger activity appears to adversely impact bus performance in the morning and

midday time periods. For crosstown routes, alighting variation is shown to be a

significant source of delay variation in all time periods. The finding that alighting

variation has a greater impact on bus performance than boarding variation is consistent

with research by Strathman and Hopper (1993), but contradicts research by Abkowitz

and Engelstein (1983, 1984) which found boardings to have a larger effect. Delay

variation at time points caused by lift operation variation is found to be important in

the midday time period for both radial and crosstown routes. While is it impossible

for schedulers to know in advance when lift operations will occur, it appears that the

midday time period demands further attention. Link speed variation was found to be

an important determinant of delay variation on radial routes in all time periods except

for the a.m. peak time period and was also found to be an important determinant of

delay variation on crosstown routes during peak time periods. These findings suggest

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that interference with vehicular traffic and/or traffic signals are important sources of

delay variation.

Tri-Met should consider expending resources to reduce the amount of delay

variation at time points because of potential benefits to passengers. Efforts to reduce

delay variation typically take one of two forms. Active intervention involves making

decisions in real time to restore service to schedule or to improve headway regularity.

Corrective measures that could be taken include such actions as vehicle holding, stop

skipping, overtaking the prior bus, and short-turning. Descriptions of control actions

and the appropriate contexts in which to apply them have been provided by a number

of researchers (Turnquist, 1982, Abkowitz & Lepofsky, 1988; Levinson, 1991;

Wilson, Macchi, Fellows & Deckoff, 1992). Longer-term strategies to reduce delay

variation might focus on such strategies as driver training, improving fare payment

methods, or even adding additional service. One technological improvement that has

not been actively pursued by North American transit providers concerns the provision

of real-time headway regularity information to operators, similar to the way in which

BDS currently displays schedule adherence information. This technology would allow

operators to modify driving bus speeds and stopping activity to improve headway

regularity during peak time periods of operation.

5.3.2 Passenger Demand Models

The passenger demand models contain relatively few policy variables, and

even fewer that proved significant. The most likely policy variables in the demand

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models from the perspective of transit service planning are the amount of scheduled

service and the number of scheduled stops. Because the unit of observation refers to

individual bus trips departing time points, the question of whether an increase in the

amount of scheduled service leads to an increase in demand is outside the scope of this

research. Increasing the number of scheduled stops is not a viable option for

increasing demand because the variable did not prove significant across all time

periods in either the radial or crosstown models. Additionally, increasing the number

of scheduled stops has an important drawback in that it results in increased travel time

for other passengers. Since the number of unscheduled stops has little bearing on

demand in any of the models except for the radial midday model and the crosstown

evening model, stop consolidation might prove to be a realistic option for streamlining

service either during peak time periods or across all time periods. The question of

whether delay variation at time points influences time point-level demand on

individual trips is not supported by the findings of this study.

The results for the radial time point-level transit patronage models indicate that

a number of factors likely to result in increased bus transit patronage are external to

the agency. In particular, the models suggest that increases in population,

employment, and the number of zero auto-ownership households will result in sizeable

increases in patronage. Regional land use policies that serve to increase population

and employment densities and reduce auto ownership will have a positive impact on

transit ridership.

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The results for the crosstown demand models are more perplexing given

difficulties explaining demand on the highest ridership routes in the Tri-Met system.

The only variables that appear to consistently explain demand on crosstown routes are

the number of zero auto-ownership households and the particular segment of the route.

Downstream population was found to be a significant determinant of demand on

crosstown routes, but is of limited usefulness because few persons travel from one end

of the route to the other. The variable for the number of complimentary radial routes

did not prove significant in any models except for the evening time period. Since a

large part of the demand for transit on crosstown routes involves transfer activity to

and from radial routes, a better method for controlling for the effects of transfer

passengers is necessary.

5.4 Directions for Future Research

A number of suggestions for improving upon the models developed in this

research are given, as well as directions for future research. One of the questions that

this research sought to answer was whether unreliable bus service adversely affects

passenger demand. The time point is not the appropriate level of analysis to answer

such a question. This is because of spatial inconsistencies inherent in the relationship

between demand and service reliability. The models developed in this study sought to

explain the determinants of demand on bus routes at the time point level of analysis.

The variable for delay variation at the previous time point was only one of several

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variables of interest. Another type of study is one that focuses on a single policy

variable on the left hand side of the equation. This type of study would require a

fundamentally different model specification and would perhaps better isolate the

effects of service quality on demand. A time series model would also prove useful for

answering the question of whether unreliable bus service affects passenger demand. A

time series model would enable the researcher to determine how changes in delay

variability affect passenger demand over time. Another type of study that should be

considered is a pre-post analysis. A researcher could analyze changes in passenger

activity over 2 separate time periods for a given route or set of routes before and after

a concerted effort by the agency to improve service quality.

Although a considerable amount of data were collected and processed for use

in the analysis, even larger quantities of data are desired. One improvement would be

to have more routes represented in the analysis besides 5 radial and 2 crosstown

routes. This would serve to increase the amount of variability between the dependent

variables and a number of the independent variables. The use of additional routes

would also result in better representation of route typology and the system in general.

At the time of data collection, relatively few bus routes were APC equipped. While

APC deployment has continued at Tri-Met, gaps in coverage still remain. At present

there are still only 2 crosstown routes that have full APC coverage. This study also

brought to light the limitations of using non-APC-equipped buses on trippers that

serve peak periods. This means that passenger activity is not collected on a large

portion of trips operating on "APC equipped" routes during peak periods. Another

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improvement would be to treat radial through routes as single routes instead of de-

linking them downtown. This would serve to increase the amount of variation

between the dependent variable and the independent variables because delays tend to

increase with distance. It would also be more representative of real world conditions

since the majority or radial routes in the Tri-Met system are radial through routes. The

data used in this analysis were collected over a period of 19 weekdays. Due to issues

surrounding data collection, processing, and integration, many of the variables

measured as variances represent only a few days’ worth of observations. For future

research, it is recommended that data be collected for at least one full sign-up period.

This would produce approximately 60 weekday observations that would result in more

robust measures of variance. In particular, it would diminish the effect of extreme

values (outliers) in the variables.

Another limitation of this study is that proxy variables were used in place of

more desirable measures. The three main variables that can be improved upon are

transfer activity, link travel speed, and destination attractiveness on crosstown routes.

Since this study began, Tri-Met has developed a better method for calculating link

travel speed using an algorithm that controls for the amount of distance between time

points. An ideal transfer activity variable would use actual passenger counts arriving

from buses that intersect the study routes when they converge in space and time. A

more precise measure of destination attractiveness on crosstown routes could be

developed using information on passenger origins and destinations or an algorithm

could be developed that takes into account both distance and transfer activity potential

124

using a using a GIS-based search routine. Due to a data processing error, passenger

boardings occurring at transit centers were not assigned to the first time point on bus

routes that originate at transit centers. While this had no effect on the transit service

reliability models, it did have consequences for the passenger demand models.

It is also apparent that more attention needs to be given to passenger loads and

their relationship to both passenger demand and service reliability. In the case of

passenger demand analysis, the relationship between passenger loads and service

supply needs to be explored in greater detail. With respect to transit service reliability,

passenger loads likely influence boarding and alighting rates and could possibly have

an adverse effect on bus performance. Another area that demands further

investigation concerns analysis of load variation. This is because no econometric

studies are known to exist that seek to explain the determinants of load variation.

5.5 Contributions to Research

The models developed in the study represent a first attempt at analyzing

passenger demand and transit service reliability at the time point level of analysis

using data pertaining to individual bus trips. It is shown that there are stark

differences between route and time point-level modeling and that each has its own set

of strengths and weaknesses. There does not appear to be an optimal scale in which to

analyze the relationships between demand, service supply, and service quality in a

simultaneous system. Another contribution of the models developed in this research is

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that the observations refer to individual bus trips. Theoretically, this is the correct

summary level because both unreliable service and the demand for transit are trip

specific. Route-level demand models are useful for analyzing the determinants of

demand and extrapolating the results to the system level. An important difference in

time point-level modeling is that the progression of a vehicle from one time point to

the next is of particular concern. Time point-level demand models are thus more

useful for analyzing the determinants of demand as they relate to individual routes.

Much of the data used in this analysis underwent extensive processing using a

GIS in order to relate data from disparate sources to a common unit of observation. It

is shown how disaggregate information can be used to more precisely allocate

socioeconomic and land use information to transit service areas. The actual allocation

method depends upon whether the allocated variable represents point data or

polygonal data. A method for controlling for accessibility to other bus routes is

developed and incorporated into the allocation process. Additionally, it is shown how

competition between bus routes can be controlled for in the allocation process.

The analysis uses archived operations data in a manner that provides feedback

to service planning, scheduling, and operations control. The findings of the time

point-level transit service reliability models suggest that efforts to control delay will

produce benefits to passengers in the form of more reliable service. Reductions in

delay resulting from control actions at early points along a route will tend to remain

constant as vehicles progress along a route. The findings of the time point-level

126

demand models suggest that socioeconomic and land use characteristics are more

important to demand than factors directly under the control of the transit agency.

The models developed in this research attempt to more closely address transit

service reliability from the perspective of passengers. Rather than using a discrete

measure of bus performance such as OTP, this study sought to explain variability in

headway delay and departure delay. A distinction was made according to service

frequency about the appropriate service reliability variable to use in the equations. As

such, headway delay variation was used as the dependent variable in the peak time

period models and departure delay variation in the off-peak time period models.

Over the past several years, Tri-Met has made considerable capital

expenditures to implement advanced transportation and communications technologies

capable of improving the quality of service provided to passengers. Passengers that

receive high quality bus service will likely remain loyal customers. Because time is

money from the perspective of passengers, high quality service equates with

predictable service. At the same time, reliable bus service represents an efficient use

of agency resources because there are fewer deviations from the operations plan.

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134

APPENDIX A: SAMPLE DATA SET

C RTE DIR TRIP TP TOD STOP HWS ONX ONV OFFV DDV DDPV HWDV1 104 0 1180 1 2 14 15 10.111 17.111 47.278 31.277 22.806 30.0262 104 0 1180 2 2 12 15 6.222 10.694 3.750 37.338 31.277 34.6943 104 0 1180 3 2 18 15 7.333 8.250 14.944 37.608 37.338 36.1764 104 0 1180 4 2 14 15 4.556 16.278 7.361 32.240 37.608 27.3895 104 0 1180 5 2 9 15 1.778 1.694 7.111 32.216 32.240 43.6246 104 0 1180 6 2 13 30 2.500 5.143 11.143 18.701 18.608 11.3277 104 0 1180 7 2 16 30 1.000 1.429 4.696 18.925 18.701 10.1898 104 0 1190 1 2 14 15 6.600 10.267 18.400 23.171 7.102 67.5109 104 0 1190 2 2 12 15 3.200 6.622 6.178 24.828 23.171 75.37210 104 0 1190 3 2 18 15 4.200 18.844 8.278 27.194 24.828 79.58411 104 0 1190 4 2 14 15 1.900 4.544 4.844 29.881 27.194 85.48912 104 0 1190 5 2 9 15 0.400 0.489 8.933 30.679 29.881 91.77213 104 0 1200 1 2 14 15 13.444 32.278 45.000 12.072 9.049 41.48314 104 0 1200 2 2 12 15 3.000 7.250 6.528 16.363 12.072 46.91215 104 0 1200 3 2 18 15 6.222 17.444 57.944 21.156 16.363 54.04316 104 0 1200 4 2 14 15 5.667 14.500 27.500 27.060 21.156 77.30617 104 0 1200 5 2 9 15 3.667 6.750 4.361 30.171 27.060 83.63618 104 0 1200 6 2 13 30 3.556 7.278 4.861 30.391 30.171 38.48519 104 0 1200 7 2 16 30 0.667 0.750 15.000 33.718 30.391 41.25720 104 0 1210 1 2 14 15 6.143 8.476 59.143 0.320 0.542 6.39721 104 0 1210 2 2 12 15 0.429 0.619 4.333 0.299 0.320 9.79522 104 0 1210 3 2 18 15 1.857 1.810 14.143 0.217 0.299 14.76823 104 0 1210 4 2 14 15 1.000 0.667 2.905 0.533 0.217 14.30924 104 0 1210 5 2 9 15 1.000 2.333 6.952 0.349 0.533 18.45925 104 0 1220 1 2 14 15 7.364 9.255 25.873 4.780 4.267 7.41426 104 0 1220 2 2 12 15 3.818 5.964 4.655 6.633 4.780 8.04927 104 0 1220 3 2 18 15 8.545 12.473 2.218 6.565 6.633 7.01828 104 0 1220 4 2 14 16 5.091 9.691 6.873 9.608 6.565 9.96229 104 0 1220 5 2 9 16 2.727 3.218 7.418 9.757 9.608 7.48430 104 0 1220 6 2 13 31 4.200 5.733 3.733 8.163 7.685 34.33631 104 0 1220 7 2 16 31 1.200 0.844 9.344 11.435 8.163 39.94632 104 0 1230 1 2 14 15 10.400 23.156 44.900 4.927 3.908 9.64633 104 0 1230 2 2 12 15 3.500 8.056 5.378 5.092 4.927 8.46334 104 0 1230 3 2 18 15 5.700 10.456 17.211 6.809 5.092 9.04935 104 0 1230 4 2 14 15 3.100 4.989 8.678 9.178 6.809 11.14036 104 0 1230 5 2 9 15 1.500 9.389 21.956 12.701 9.178 14.76337 104 0 1240 1 2 14 15 16.909 180.291 238.255 119.724 7.384 37.17638 104 0 1240 2 2 12 15 4.727 10.618 62.291 108.423 119.724 39.41739 104 0 1240 3 2 18 15 5.182 20.164 12.618 96.253 108.423 45.59340 104 0 1240 4 2 14 15 4.455 11.473 16.473 80.198 96.253 54.50241 104 0 1240 5 2 9 15 2.909 5.691 3.800 73.393 80.198 59.79142 104 0 1240 6 2 13 30 3.667 6.500 16.250 72.018 83.641 71.82043 104 0 1240 7 2 16 30 0.111 0.111 17.861 64.024 72.018 69.19444 104 0 1250 1 2 14 15 10.000 75.667 102.571 1.236 5.438 33.21445 104 0 1250 2 2 12 15 2.857 4.143 4.333 1.948 1.236 26.179

135

C HWDPV NROV USSV LIFTV EVNTV MPHV DIST COMPX COMPR TC AUTO1 15.400 0.000 0.750 0.111 0.111 10.046 116.56 1 -99 1 662 30.026 0.000 1.861 0.000 0.111 4.458 78.65 1 -99 0 1823 34.694 0.000 0.528 0.000 0.111 3.411 117.22 2 -99 0 2134 36.176 0.000 0.750 0.000 0.111 10.246 105.55 0 -99 0 895 27.389 0.000 0.250 0.000 0.111 17.660 57.92 1 -99 0 976 37.857 0.000 0.214 0.000 0.000 9.176 100.72 0 -99 0 1057 11.327 0.000 1.929 0.000 0.000 2.082 132.04 0 -99 1 848 20.723 0.278 2.044 0.000 0.000 5.116 116.56 1 -99 1 669 67.510 0.278 0.489 0.000 0.000 4.328 78.65 1 -99 0 182

10 75.372 0.278 1.556 0.000 0.000 2.524 117.22 2 -99 0 21311 79.584 0.278 0.489 0.000 0.000 10.162 105.55 0 -99 0 8912 85.489 0.278 0.178 0.000 0.000 16.523 57.92 1 -99 0 9713 21.221 0.250 3.111 0.111 0.194 2.863 116.56 1 -99 1 6614 41.483 0.250 0.194 0.000 0.194 12.762 78.65 1 -99 0 18215 46.912 0.250 0.861 0.444 0.250 1.077 117.22 2 -99 0 21316 54.043 0.250 0.528 0.111 0.250 13.048 105.55 0 -99 0 8917 77.306 0.250 0.278 0.000 0.250 9.554 57.92 1 -99 0 9718 83.636 0.250 0.444 0.000 0.250 6.403 100.72 0 -99 0 10519 38.485 0.250 0.528 0.111 0.250 12.744 132.04 0 -99 1 8420 5.001 0.000 1.619 0.000 0.000 0.450 116.56 1 -99 1 6621 6.397 0.000 0.143 0.000 0.000 3.841 78.65 1 -99 0 18222 9.795 0.000 0.905 0.000 0.000 1.024 117.22 2 -99 0 21323 14.768 0.000 0.571 0.000 0.000 3.096 105.55 0 -99 0 8924 14.309 0.000 0.000 0.000 0.000 14.535 57.92 1 -99 0 9725 4.750 0.218 1.473 0.091 0.000 5.105 116.56 1 -99 1 6626 7.414 0.218 0.455 0.091 0.000 4.624 78.65 1 -99 0 18227 8.049 0.218 1.291 0.091 0.000 2.914 117.22 2 -99 0 21328 7.018 0.218 0.273 0.000 0.000 4.392 105.55 0 -99 0 8929 9.962 0.218 0.655 0.000 0.000 23.189 57.92 1 -99 0 9730 8.311 0.233 0.178 0.400 0.000 8.719 100.72 0 -99 0 10531 34.336 0.233 0.456 0.000 0.000 15.656 132.04 0 -99 1 8432 5.004 0.000 1.878 0.178 0.000 4.244 116.56 1 -99 1 6633 9.646 0.000 0.500 0.000 0.000 1.724 78.65 1 -99 0 18234 8.463 0.000 3.211 0.100 0.000 2.732 117.22 2 -99 0 21335 9.049 0.000 0.456 0.000 0.000 13.651 105.55 0 -99 0 8936 11.140 0.000 0.100 0.000 0.000 18.219 57.92 1 -99 0 9737 10.536 0.255 1.418 0.091 0.091 4.909 116.56 1 -99 1 6638 37.176 0.255 0.673 0.000 0.091 7.328 78.65 1 -99 0 18239 39.417 0.255 1.018 0.000 0.091 8.109 117.22 2 -99 0 21340 45.593 0.255 0.473 0.000 0.091 8.158 105.55 0 -99 0 8941 54.502 0.255 0.091 0.000 0.091 39.236 57.92 1 -99 0 9742 62.338 0.250 0.194 0.000 0.111 8.525 100.72 0 -99 0 10543 71.820 0.250 0.444 0.111 0.111 18.915 132.04 0 -99 1 8444 25.843 0.143 1.952 0.000 0.000 6.094 116.56 1 -99 1 6645 33.214 0.143 0.667 0.000 0.000 1.866 78.65 1 -99 0 182

136

C POPD POP EMPD EMP POPI EMPDI EMPO POPDO1 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.172 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.553 91.41 32.14 57.14 16.80 0.00 0.00 16.80 91.414 68.21 23.19 42.56 14.58 0.00 0.00 14.58 68.215 50.16 18.05 33.77 8.79 0.00 0.00 8.79 50.166 20.93 29.24 12.06 21.71 0.00 0.00 21.71 20.937 0.00 20.93 0.00 12.06 0.00 0.00 12.06 0.008 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.179 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.55

10 91.41 32.14 57.14 16.80 0.00 0.00 16.80 91.4111 68.21 23.19 42.56 14.58 0.00 0.00 14.58 68.2112 50.16 18.05 33.77 8.79 0.00 0.00 8.79 50.1613 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.1714 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.5515 91.41 32.14 57.14 16.80 0.00 0.00 16.80 91.4116 68.21 23.19 42.56 14.58 0.00 0.00 14.58 68.2117 50.16 18.05 33.77 8.79 0.00 0.00 8.79 50.1618 20.93 29.24 12.06 21.71 0.00 0.00 21.71 20.9319 0.00 20.93 0.00 12.06 0.00 0.00 12.06 0.0020 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.1721 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.5522 91.41 32.14 57.14 16.80 0.00 0.00 16.80 91.4123 68.21 23.19 42.56 14.58 0.00 0.00 14.58 68.2124 50.16 18.05 33.77 8.79 0.00 0.00 8.79 50.1625 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.1726 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.5527 91.41 32.14 57.14 16.80 0.00 0.00 16.80 91.4128 68.21 23.19 42.56 14.58 0.00 0.00 14.58 68.2129 50.16 18.05 33.77 8.79 0.00 0.00 8.79 50.1630 20.93 29.24 12.06 21.71 0.00 0.00 21.71 20.9331 0.00 20.93 0.00 12.06 0.00 0.00 12.06 0.0032 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.1733 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.5534 91.41 32.14 57.14 16.80 0.00 0.00 16.80 91.4135 68.21 23.19 42.56 14.58 0.00 0.00 14.58 68.2136 50.16 18.05 33.77 8.79 0.00 0.00 8.79 50.1637 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.1738 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.5539 91.41 32.14 57.14 16.80 0.00 0.00 16.80 91.4140 68.21 23.19 42.56 14.58 0.00 0.00 14.58 68.2141 50.16 18.05 33.77 8.79 0.00 0.00 8.79 50.1642 20.93 29.24 12.06 21.71 0.00 0.00 21.71 20.9343 0.00 20.93 0.00 12.06 0.00 0.00 12.06 0.0044 151.17 2.51 82.73 57.40 0.00 0.00 57.40 151.1745 123.55 27.63 73.94 8.79 0.00 0.00 8.79 123.55

137

APPENDIX B: DESCRIPTIVE STATISTICS

RADIAL RELIABILITY: AM (IN) NAME N MEAN ST DEV VAR MIN MAXHWDV 550 7.074 7.664 58.737 0.270 93.329HWS 550 9.176 4.246 18.025 2.000 32.000HWDPV 550 5.604 5.803 33.670 0.028 76.928ONV 550 19.065 25.456 648.000 0.000 179.810OFFV 550 17.327 34.460 1187.500 0.000 244.620DIST 550 78.379 24.615 605.900 31.510 147.360USSV 550 0.535 0.636 0.405 0.000 5.018LIFTV 550 0.018 0.105 0.011 0.000 2.118EVNTV 550 0.017 0.041 0.002 0.000 0.250NROV 550 0.125 0.103 0.011 0.000 0.300MPHV 550 6.255 10.594 112.220 0.311 131.350RTE4 550 0.142 0.349 0.122 0.000 1.000RTE8 550 0.104 0.305 0.093 0.000 1.000RTE14 550 0.276 0.448 0.200 0.000 1.000RTE15 550 0.258 0.438 0.192 0.000 1.000RTE104 550 0.220 0.415 0.172 0.000 1.000 RADIAL RELIABILITY: MIDDAY (BOTH) NAME N MEAN ST DEV VAR MIN MAXDDV 1630 9.327 11.674 136.280 0.101 119.720HWS 1630 14.269 4.166 17.353 7.000 36.000DDPV 1630 7.560 10.390 107.960 0.023 119.720ONV 1630 16.678 24.441 597.370 0.000 375.690OFFV 1630 16.542 21.899 479.580 0.000 269.780DIST 1630 79.288 26.652 710.350 28.220 164.950USSV 1630 0.666 0.696 0.484 0.000 7.255LIFTV 1630 0.060 0.121 0.015 0.000 1.368EVNTV 1630 0.028 0.055 0.003 0.000 0.263NROV 1630 0.122 0.096 0.009 0.000 0.300MPHV 1630 7.639 13.358 178.420 0.147 177.600IN 1630 0.506 0.500 0.250 0.000 1.000RTE4 1630 0.184 0.388 0.150 0.000 1.000RTE8 1630 0.179 0.384 0.147 0.000 1.000RTE14 1630 0.225 0.417 0.174 0.000 1.000RTE15 1630 0.221 0.415 0.172 0.000 1.000RTE104 1630 0.191 0.394 0.155 0.000 1.000

138

RADIAL RELIABILITY: PM (OUT) NAME N MEAN ST DEV VAR MIN MAXHWDV 558 21.695 16.857 284.160 0.361 179.230HWS 558 9.703 4.610 21.247 1.000 37.000HWDPV 558 17.842 12.620 159.270 0.238 71.177ONV 558 26.297 39.866 1589.300 0.000 234.840OFFV 558 25.642 26.047 678.450 0.000 195.580DIST 558 81.515 27.848 775.490 28.220 172.360USSV 558 0.773 0.783 0.613 0.000 5.891LIFTV 558 0.053 0.164 0.027 0.000 2.909EVNTV 558 0.057 0.085 0.007 0.000 0.300NROV 558 0.115 0.109 0.012 0.000 0.333MPHV 558 6.646 19.415 376.960 0.002 429.030RTE4 558 0.172 0.378 0.143 0.000 1.000RTE8 558 0.181 0.385 0.149 0.000 1.000RTE14 558 0.222 0.416 0.173 0.000 1.000RTE15 558 0.235 0.424 0.180 0.000 1.000RTE104 558 0.190 0.393 0.154 0.000 1.000 RADIAL RELIABILITY: EVENING (BOTH) NAME N MEAN ST DEV VAR MIN MAXDDV 726 8.807 8.281 68.581 0.010 48.353HWS 726 15.124 3.952 15.615 6.000 45.000DDPV 726 7.401 7.651 58.535 0.008 45.559ONV 726 10.260 15.616 243.870 0.000 137.360OFFV 726 10.721 13.003 169.090 0.000 123.600DIST 726 79.393 26.674 711.510 28.220 164.950USSV 726 0.510 0.613 0.376 0.000 5.878LIFTV 726 0.043 0.117 0.014 0.000 1.983EVNTV 726 0.023 0.050 0.002 0.000 0.300NROV 726 0.130 0.108 0.012 0.000 0.333MPHV 726 7.229 12.692 161.100 0.098 203.700IN 726 0.475 0.500 0.250 0.000 1.000RTE4 726 0.197 0.398 0.158 0.000 1.000RTE8 726 0.191 0.394 0.155 0.000 1.000RTE14 726 0.207 0.405 0.164 0.000 1.000RTE15 726 0.207 0.405 0.164 0.000 1.000RTE104 726 0.198 0.399 0.159 0.000 1.000

139

CROSSTOWN RELIABILITY: AM (BOTH) NAME N MEAN ST DEV VAR MIN MAXHWDV 605 12.017 136.180 0.129 89.539HWS 605 11.610 3.090 9.550 4.000 40.000HWDPV 605 9.653 9.414 88.618 0.071 58.296ONV 605 18.077 26.425 698.280 0.000 268.500OFFV 605 20.036 35.949 1292.300 0.000 277.740DIST 605 100.490 34.730 1206.200 38.200 166.290USSV 605 0.497 0.566 0.320 0.000 5.143LIFTV 605 0.020 0.073 0.005 0.000 0.750EVNTV 605 0.031 0.062 0.004 0.000 0.333NROV 605 0.115 0.107 0.012 0.000 0.333MPHV 605 5.960 7.515 56.468 0.165 64.622ES 605 0.499 0.500 0.250 0.000 1.000RTE72 605 0.521 0.500 0.250 0.000 1.000RTE75 605 0.479 0.500 0.250 0.000 1.000

11.670

CROSSTOWN RELIABILITY: MIDDAY (BOTH) NAME N MEAN ST DEV VAR MIN MAXDDV 1195 6.526 6.569 43.150 0.012 55.361HWS 1195 11.631 3.048 9.290 2.000 31.000DDPV 1195 5.245 5.644 31.852 0.012 41.219ONV 1195 21.530 29.000 841.000 0.141 346.580OFFV 1195 19.309 22.217 493.580 0.242 156.190DIST 1195 100.140 34.586 1196.200 38.200 166.290USSV 1195 0.586 0.556 0.309 0.000 4.364LIFTV 1195 0.045 0.116 0.013 0.000 2.000EVNTV 1195 0.028 0.056 0.003 0.000 0.286NROV 1195 0.103 0.099 0.010 0.000 0.333MPHV 1195 7.075 16.252 264.140 0.371 245.860ES 1195 0.497 0.500 0.250 0.000 1.000RTE72 1195 0.573 0.495 0.245 0.000 1.000RTE75 1195 0.427 0.495 0.245 0.000 1.000 CROSSTOWN RELIABILITY: PM (BOTH) NAME N MEAN ST DEV VAR MIN MAXHWDV 685 20.489 17.493 306.020 0.817 137.940HWS 685 9.495 3.500 12.247 2.000 60.000HWDPV 685 16.756 14.487 209.870 0.137 82.082ONV 685 24.802 25.286 639.390 0.000 220.460OFFV 685 21.768 21.200 449.420 0.220 155.930DIST 685 100.090 34.625 1198.900 38.200 166.290USSV 685 0.515 0.544 0.296 0.000 6.571LIFTV 685 0.036 0.087 0.008 0.000 0.900EVNTV 685 0.050 0.072 0.005 0.000 0.269NROV 685 0.095 0.098 0.010 0.000 0.333MPHV 685 6.851 14.008 196.220 0.460 223.440ES 685 0.495 0.500 0.250 0.000 1.000RTE72 685 0.564 0.496 0.246 0.000 1.000RTE75 685 0.437 0.496 0.246 0.000 1.000

140

CROSSTOWN RELIABILITY: EVENING (BOTH) NAME N MEAN ST DEV VAR MIN MAXDDV 487 8.995 8.804 77.515 0.133 67.228HWS 487 13.704 1.907 3.637 9.000 17.000DDPV 487 7.612 7.632 58.240 0.044 54.243ONV 487 12.177 13.277 176.270 0.000 75.600OFFV 487 12.104 12.404 153.850 0.071 133.810DIST 487 99.767 34.694 1203.700 38.200 166.290USSV 487 0.451 0.442 0.195 0.000 3.474LIFTV 487 0.025 0.083 0.007 0.000 1.238EVNTV 487 0.036 0.061 0.004 0.000 0.269NROV 487 0.089 0.101 0.010 0.000 0.278MPHV 487 13.380 34.323 1178.100 0.322 341.000ES 487 0.507 0.500 0.250 0.000 1.000RTE72 487 0.517 0.500 0.250 0.000 1.000RTE75 487 0.483 0.500 0.250 0.000 1.000 RADIAL DEMAND: AM (IN) NAME N MEAN ST DEV VAR MIN MAXONX 550 8.808 6.847 46.884 0.000 35.533HWS 550 9.176 4.246 18.025 2.000 32.000HWDPV 550 5.604 5.803 33.670 0.028 76.928STOP 550 10.355 4.037 16.298 2.000 19.000POPI 550 17.071 12.449 154.980 0.140 40.310EMPDI 550 46.747 30.067 904.020 0.000 112.830TC 550 0.282 0.450 0.203 0.000 1.000COMPX 550 1.011 0.672 0.452 0.000 2.000AUTO 550 1.439 1.331 1.773 0.020 5.130RTE4 550 0.142 0.349 0.122 0.000 1.000RTE8 550 0.104 0.305 0.093 0.000 1.000RTE14 550 0.276 0.448 0.200 0.000 1.000RTE15 550 0.258 0.438 0.192 0.000 1.000RTE104 550 0.220 0.415 0.172 0.000 1.000

141

RADIAL DEMAND: MIDDAY (BOTH) NAME N MEAN ST DEV VAR MIN MAXONX 1630 6.463 5.434 29.522 0.000 53.500HWS 1630 14.269 4.166 17.353 7.000 36.000DDPV 1630 7.560 10.390 107.960 0.023 119.720STOP 1630 10.666 3.938 15.511 2.000 20.000POPI 1630 8.301 11.963 143.120 0.000 40.310EMPDI 1630 22.209 30.351 921.210 0.000 112.830EMPO 1630 7.600 11.957 142.970 0.000 57.400POPDO 1630 26.110 38.894 1512.700 0.000 151.170AUTO 1630 1.408 1.272 1.617 0.020 5.130TC 1630 0.272 0.445 0.198 0.000 1.000COMPX 1630 1.002 0.586 0.343 0.000 2.000IN 1630 0.506 0.500 0.250 0.000 1.000RTE4 1630 0.184 0.388 0.150 0.000 1.000RTE8 1630 0.179 0.384 0.147 0.000 1.000RTE14 1630 0.225 0.417 0.174 0.000 1.000RTE15 1630 0.221 0.415 0.172 0.000 1.000RTE104 1630 0.191 0.394 0.155 0.000 1.000 RADIAL DEMAND: PM (OUT) NAME N MEAN ST DEV VAR MIN MAXONX 558 8.319 10.351 107.150 0.000 54.750HWS 558 9.703 4.610 21.247 1.000 37.000HWDPV 558 17.842 12.620 159.270 0.238 71.177STOP 558 10.728 3.758 14.120 2.000 20.000EMPO 558 15.402 13.018 169.470 1.240 57.400POPDO 558 52.892 40.706 1657.000 0.000 151.170AUTO 558 1.413 1.238 1.532 0.130

0.219

0.149

4.960TC 558 0.254 0.436 0.190 0.000 1.000COMPX 558 0.962 0.468 0.000 2.000RTE4 558 0.172 0.378 0.143 0.000 1.000RTE8 558 0.181 0.385 0.000 1.000RTE14 558 0.222 0.416 0.173 0.000 1.000RTE15 558 0.235 0.424 0.180 0.000 1.000RTE104 558 0.190 0.393 0.154 0.000 1.000

142

1.000

RADIAL DEMAND: EVENING (BOTH) NAME NMEAN ST DEV VAR MIN MAX ONX 726 4.604 5.524 30.509 0.000 49.917HWS 726 15.124 3.952 15.615 6.000 45.000DDPV 726 7.401 7.651 58.535 0.008 45.559STOP 726 10.729 3.950 15.602 2.000 20.000POPI 726 7.799 11.749 138.030 0.000 40.310EMPDI 726 20.481 29.468 868.350 0.000 112.830EMPO 726 8.053 12.228 149.530 0.000 57.400POPDO 726 28.742 40.286 1623.000 0.000 151.170AUTO 726 1.422 1.268 1.608 0.020 5.130TC 726 0.266 0.442 0.195 0.000 COMPX 726 1.008 0.594 0.353 0.000 2.000IN 726 0.475 0.500 0.250 0.000 1.000RTE4 726 0.197 0.398 0.158 0.000 1.000RTE8 726 0.191 0.394 0.155 0.000 1.000RTE14 726 0.207 0.405 0.164 0.000 1.000RTE15 726 0.207 0.405 0.164 0.000 1.000RTE104 726 0.198 0.399 0.159 0.000 1.000 CROSSTOWN DEMAND: AM (BOTH) NAME N MEAN ST DEV VAR MIN MAXONX 605.000 7.163 5.350 28.617 0.000 29.857HWS 605.000 11.610 3.090 9.550 4.000 40.000HWDPV 605.000 9.653 9.414 88.618 0.071 58.296STOP 605.000 13.369 4.412 19.462 5.000 21.000POP 605.000 18.480 8.237

AUTO 0.000

67.843 3.990 38.370EMPD 605.000 42.824 27.594 761.430 0.000 99.780

605.000 1.144 0.598 0.357 0.290 2.780COMPR 605.000 2.478 1.167 1.363 5.000TC 605.000 0.154 0.361 0.130 0.000 1.000ES 605.000 0.499 0.500 0.250 0.000 1.000RTE75_LM 605.000 0.192 0.394 0.155 0.000 1.000RTE75_39 605.000 0.288 0.453 0.205 0.000 1.000RTE72_82 605.000 0.289 0.454 0.206 0.000 1.000RTE72_KL 605.000 0.231 0.422 0.178 0.000 1.000

143

CROSSTOWN DEMAND: MIDDAY (BOTH) NAME N MEAN ST DEV VAR MIN MAXONX 1195.000 7.554

1195.000

5.346 28.577 0.154 45.467HWS 1195.000 11.631 3.048 9.290 2.000 31.000DDPV 1195.000 5.245 5.644 31.852 0.012 41.219STOP 1195.000 13.312 4.371 19.103 5.000 21.000POP 1195.000 18.549 8.338 69.523 3.990 38.370EMPD 43.468 27.952 781.310 0.000 99.780AUTO 1195.000 1.159 0.612 0.375 0.290 2.780COMPR 1195.000 2.458 1.159 1.342 0.000 5.000TC 1195.000 0.150 0.357 0.127 0.000 1.000ES 1195.000 0.497 0.500 0.250 0.000 1.000RTE75_LM 1195.000 0.171 0.376 0.142 0.000 1.000RTE75_39 1195.000 0.256 0.437 0.191 0.000 1.000RTE72_82 1195.000 0.320 0.467 0.218 0.000 1.000RTE72_KL 1195.000 0.254 0.435 0.189 0.000 1.000 CROSSTOWN DEMAND: PM (BOTH) NAME N MEAN ST DEV VAR MIN MAXONX 685.000 7.957 5.513 30.389 0.000 38.125HWS 685.000

82.082

8.336

AUTO

CROSSTOWN DEMAND: EVENING (BOTH)

9.495 3.500 12.247 2.000 60.000HWDPV 685.000 16.756 14.487 209.870 0.137 STOP 685.000 13.312 4.384 19.218 5.000 21.000POP 685.000 18.535 69.482 3.990 38.370EMPD 685.000 43.248 27.815 773.650 0.000 99.780

685.000 1.157 0.611 0.373 0.290 2.780COMPR 685.000 2.458 1.150 1.322 0.000 5.000TC 685.000 0.149 0.356 0.127 0.000 1.000ES 685.000 0.495 0.500 0.250 0.000 1.000RTE75_LM 685.000 0.175 0.380 0.145 0.000 1.000RTE75_39 685.000 0.261 0.440 0.193 0.000 1.000RTE72_82 685.000 0.314 0.464 0.216 0.000 1.000RTE72_KL 685.000 0.250 0.433 0.188 0.000 1.000

NAME N MEAN ST DEV VAR MIN MAXONX 487.000 5.109 3.720 13.839 0.000 18.500HWS 487.000 13.704 1.907 3.637 9.000 17.000DDPV 487.000 7.612 7.632 58.240 0.044 54.243STOP 487.000 13.170 4.360 19.010 5.000

43.656 719.840 0.000 99.780

487.0000.355

21.000POP 487.000 18.457 8.322 69.251 3.990 38.370EMPD 487.000 26.830AUTO 487.000 1.148 0.597 0.356 0.290 2.780COMPR 2.474 1.138 1.295 0.000 5.000TC 487.000 0.148 0.126 0.000 1.000ES 487.000 0.507 0.500 0.250 0.000 1.000RTE75_LM 487.000 0.193 0.395 0.156 0.000 1.000RTE75_39 487.000 0.290 0.454 0.206 0.000 1.000RTE72_82 487.000 0.287 0.453 0.205 0.000 1.000RTE72_KL 487.000 0.230 0.421 0.177 0.000 1.000

144

APPENDIX C: MODEL ELASTICITIES

RADIAL RELIABILITY: AM (IN) CROSSTOWN RELIABILITY: AM (BOTH)NAME MEAN COEFF T VAL ELAST NAME MEAN COEFF T VAL ELASTHWDV 7.074 -- -- -- HWDV 12.017 -- -- --HWS 9.176 0.268 4.036 0.347 HWS 11.610 0.329 3.911 0.318HWDPV 5.604 0.750 17.850 0.595 HWDPV 9.653 0.991 35.100 0.796ONV 19.065 0.033 3.367 0.089 ONV 18.077 0.019 1.927 0.028OFFV 17.327 0.028 3.726 0.068 OFFV 20.036 0.024 3.445 0.040DIST 78.379 -0.029 -2.430 -0.321 DIST 100.490 0.023 3.301 0.194USSV 0.535 0.876 1.990 0.066 USSV 0.497 -0.550 -1.263 -0.023LIFTV 0.018 3.475 1.550 0.009 LIFTV 0.020 2.841 0.876 0.005EVNTV 0.017 27.529 4.547 0.065 EVNTV 0.031 4.800 1.200 0.012NROV 0.125 4.191 1.788 0.074 NROV 0.115 -1.583 -0.708 -0.015MPHV 6.255 0.000 -0.002 0.000 MPHV 5.960 0.155 4.823 0.077 RADIAL RELIABILITY: MID (BOTH) CROSSTOWN RELIABILITY: MID (BOTH)NAME MEAN COEFF T VAL ELAST NAME MEAN COEFF T VAL ELASTDDV 9.327 -- -- -- DDV 6.526 -- -- --HWS 14.269 0.098 2.431 0.150 HWS 11.631 0.089 2.389 0.160DDPV 7.560 0.943 66.090 0.765 DDPV 5.245 0.988 58.720 0.794ONV 16.678 0.016 2.695 0.029 ONV 21.530 0.000 -0.167 -0.002OFFV 16.542 0.038 5.766 0.068 OFFV 19.309 0.014 3.623 0.042DIST 79.288 0.010 1.657 0.089 DIST 100.140 0.003 1.344 0.049USSV 0.666 0.589 2.718 0.042 USSV 0.586 0.268 1.794 0.024LIFTV 0.060 4.768 4.233 0.031 LIFTV 0.045 3.350 4.963 0.023EVNTV 0.028 9.041 3.515 0.027 EVNTV 0.028 7.780 4.635 0.034NROV 0.122 -0.449 -0.328 -0.006 NROV 0.103 0.092 0.117 0.002MPHV 7.639 0.040 3.968 0.033 MPHV 7.075 0.004 0.755 0.004 RADIAL RELIABILITY: PM (OUT) CROSSTOWN RELIABILITY: PM (BOTH)NAME MEAN COEFF T VAL ELAST NAME MEAN COEFF T VAL ELASTHWDV 21.695 -- -- -- HWDV 20.489 -- -- --HWS 9.703 0.688 6.211 0.308 HWS 9.495 0.968 8.578 0.449HWDPV 17.842 0.957 25.640 0.787 HWDPV 16.756 0.948 31.920 0.776ONV 26.297 -0.006 -0.491 -0.007 ONV 24.802 0.009 0.653 0.011OFFV 25.642 0.024 1.437 0.028 OFFV 21.768 0.038 2.106 0.041DIST 81.515 0.076 4.228 0.287 DIST 100.090 0.030 2.849 0.149USSV 0.773 0.079 0.132 0.003 USSV 0.515 0.732 1.092 0.018LIFTV 0.053 -5.172 -2.047 -0.013 LIFTV 0.036 2.486 0.620 0.004EVNTV 0.057 5.887 1.125 0.016 EVNTV 0.050 6.129 1.192 0.015NROV 0.115 1.356 0.329 0.007 NROV 0.095 8.076 2.233 0.037MPHV 6.646 0.057 2.694 0.018 MPHV 6.851 0.025 0.044 0.018

145

RADIAL RELIABILITY: EVE (BOTH) CROSSTOWN RELIABILITY: EVE (BOTH)NAME MEAN COEFF T VAL ELAST NAME MEAN COEFF T VAL ELASTDDV 8.807 -- -- -- DDV 8.995 -- -- --HWS 15.124 0.011 0.301 0.020 HWS 13.704 -0.029 -0.382 -0.044DDPV 7.401 0.928 47.750 0.780 DDPV 7.612 1.054 58.020 0.892ONV 10.260 -0.022 -2.340 -0.026 ONV 12.177 0.027 2.752 0.036OFFV 10.721 0.039 3.279 0.047 OFFV 12.104 0.050 4.810 0.068DIST 79.393 -0.008 -1.227 -0.071 DIST 99.767 0.007 1.943 0.074USSV 0.510 0.248 0.960 0.014 USSV 0.451 0.080 0.284 0.004LIFTV 0.043 7.638 6.583 0.038 LIFTV 0.025 1.768 1.197 0.005EVNTV 0.023 4.648 1.645 0.012 EVNTV 0.036 5.580 2.638 0.022

NROV NROV 0.130 -0.526 -0.417 -0.008 0.089 2.938 2.194 0.029MPHV 7.229 0.022 2.015 0.018 MPHV 13.380 -0.001 -0.323 -0.002

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APPENDIX D: TIME POINT OBSERVATIONS

Route Outbound Inbound Trips TP TOD Trips TP

Route 4: Fesseden 1 14 6 1 13 6 2 24 6 2 26 6

3 16 6 3 16 6 4 13 6 4 11 6 Route 8: NE 15th 1 11 7 1 17 8

2 24 7 2 25 8 3 17 7 3 12 8 4 13 7 4 12 8 Route 14: Hawthorne 1 17 6 1 31 6 2 31 6 2 30 6 3 27 6 3 16 6 4 18 6 4 15 6 Route 15: Belmont 1 16 6 1 27 6 2 3 0 6 2 30 6 3 22 6 3 16 6 4 13 6 4 12 6 Route 72: Kill./82nd 1 17 9 1 18 9 2 38 9 2 39 9 3 23 9 3 22 9 4 14 9 4 14 9 Route 75: 39th/Lomb. 1 15 10 1 14 10 2 26 10 2 25 10 3 15 10 3 15 10 4 12 10 4 13 10 Route 104: Division 1 11 7 1 20 7 2 25 7 2 27 7 3 19 7 3 13 7 4 13 7 4 11 7

TOD

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