Travel Time Reliability Analysis Using Dynamic Message...

Travel Time Reliability Analysis Using Dynamic Message SignRecordings

Neveen Shlayan (corresponding author)[email protected]

Phone: 702-524-5129

Lillian [email protected]

Omer [email protected]

Pushkin Kachroo, [email protected]

Phone: 702-895-5258

Transportation Research CenterUniversity of Nevada, Las Vegas

4054 Maryland PkwyLas Vegas, Nevada 89104

Brian Hoeft, PERegional Transportation Commission of Southern Nevada FAST

4615 West Sunset RoadLas Vegas, NV [email protected]

Phone: 702-357-6928

2661 words + 5 figures + 6 tables

July 31, 2009

Abstract

Travel time is a good indicator of the performance of a street segment or thehighway as a whole. However,solely, it lacks information about the overall performance of the transportation system. Travelers tend to givea higher value to consistency of travel times than the travel time itself in order to better plan their trip. Put inother terms, reliability of the route is of a great importance when assessing thesystem. Therefore, additionalanalysis is required on travel times. Various analysis approaches have been conducted for this purpose. Mostcommonly used are the traditional statistical methods demonstrating variability. In this paper, travel timedata on the I-15 highway Las Vegas will be analyzed using the statistical approach. Moreover, new analysismethods are proposed in this study. Travel time mean estimation, non-failure analysis, and informationtheory based reliability. The proposed methods add to the ordinary evaluation criteria of highway systems,thus, introducing new reliability measures.

Shlayan, Ratliff, Ayubi, Kachroo, Hoeft 1

INTRODUCTIONTravel time is the time that it takes users of the road system to commute from one location to a specificdestination. Considering a fixed length of a highway section, travel times directly reflect traffic conditions,such as congestion due to recurring or nonrecurring events. Trafficconditions caused by nonrecurringevents are highly unpredictable causing unexpected delays which directlyaffect travel times; the resultingvariability is referred to as “travel time reliability”. The uncertainty associatedwith travel times is of majorimportance to drivers; it is highly ranked among all influential factors of departure time choice of travelers(2). The inconsistency of travel times inflict a scheduling cost where commuters have to budget extratime when traveling a certain route (3). Therefore, travel time reliability is an imperative measure intransportation system management (10). Travel time reliability can take various quantitative measures allof which differ to a certain degree in the information they contain when evaluating the reliability of a route.The appropriate measure ought to be chosen depends on the evaluation criteria. Most researchers as well astransportation entities use standard statistical methods when defining reliability.In this paper, in addition tothe traditional reliability measures, travel time variance and confidence intervals, failure analysis approachis introduced. Moreover, information theory based approach is proposed which adds a new dimension tothe meaning of reliability. A literature survey of different travel time reliability approaches is introducedin Section 2. Four quantitative reliability measures are proposed in Section 3.In Section 4, travel timereliability on the I-15 in the Las Vegas area will be assessed based on Dynamic Message Signs (DMS)massages using the proposed methods. Discussion and conclusions are inSections 5 and 6, respectively.

LITERATURE SURVEYBogers in (2) recognizes the various reliability measures that have been used and stresses the reliabilityanalysis method depends on the application.

Nie and Fan ((9)) developed an adaptive routing strategy, named the stochastic on-time arrival(SOTA) algorithm, to target least-expected travel time as a mechanism to address the performance mea-sure of reliability.

Oh and Chung (10) study travel time variability using data from Orange County, California. Theystudy travel time variability that they compute in terms of variance in terms of

• day-to-day variability,

• within-day variability, and

• spatial variability.

They also find that travel time is correlated with standard deviation.Chen et. al. ((3)) demonstrates the relationship between travel time and level of service. They show

how the 90th percentile travel incorporates the mean and variability into a singlemeasure, and also studyhow travel time information using ITS can reduce travel uncertainty.

The median of travel times as a measure of reliability is used in Lam’s study (12) (2). Black (1)defines a travel time reliability ratio which gives an assessment of the extra time commuters must accountfor based on variance (2). Van Lint (8) defines skew as a measure of the asymmetry of the travel timedistribution and claims its importance in travel time reliability.

Cambridge Systematic (4) used buffer and planning time to measure reliability and found thatbuffer and planning time indices are very useful statistical measures. Buffer index is defined as the extratime needed to accomplish a certain trip with respect to the mean travel time; where,planning time index isan indication of the deviation of the buffer size from the ideal travel time (4).

Evidently, travel time reliability can take various measures; the optimal reliability approach choicegreatly depends on the examined aspect of the specific application. In this study, four different reliability


approaches are used to analyze travel time data on the I-15 Las Vegas area. Statistical variance, confidenceintervals, failure analysis, and information theory based approaches are used and results are compared.

RELIABILITY MEASURES AND TECHNICAL METHODSThe term “reliability” suggests repeatability or dependability. For a random experiment this would meanthat the results of an experiment are repeatable. In terms of travel-time, this would mean that if travel timeis measured repeatedly on a section we get comparable values. In general, repeatability of travel time couldbe framed in terms of time-of-day, day of the week, etc. Thus, travel time reliability is determined byconducting analysis on data measured for a certain segment.

In this study five different approaches are used in obtaining various reliability measures:

• Variability, Based on Normalized Standard Deviation,

• Analysis of Variance ANOVA

• Travel Time Mean Estimation,

• Reliability as a Measure of Non-failures, and

• Information Theory Based Approach

Variability, Based on Normalized Standard DeviationFor a given set of travel time data Equation??on a freeway section, statistical mean can be calculated givenby Equation 1; however, travel time mean is not sufficient since it does notconvey any information abouthow volatile the travel times are on the studied highway segment. Therefore, calculations of the standarddeviation given in Equation 2 are necessary in order to understand the distributive nature of travel times(13). Clearly, a lower standard deviation indicates a higher concentration of data about the mean illustratingcloser values to the mean; thus a more reliable highway segment.

τ̄ =

∑ni=0

τi

N(1)

σ =

√

∑ni=0

(τi − τ̄)2

N(2)

whereτn : travel time on a certain highway segmentτ̄ : Average travel time for the given data setσ : Standard deviation of travel times for the given data setN : Total number of data points in the data set

Analysis of Variance (ANOVA)Using ANOVA, the mean of various data sets were compared for hypothesistesting. A null hypothesis isdefined by determining a desiredα value representing the variation between the various groups tested. If theratio of the variance among the samples means to the variance within the samplesF is less thanF criticalFα value, then the null hypothesis (H0) is accepted indicating that the variation in mean falls within thedesired regions. Otherwise, the alternate hypothesis (H1)is accepted.

H0: F ≤Fα

H1: F > Fα(3)


where:

H0 : Null hypothesisH1 : Alternative hypothesis

Travel Time Mean EstimationAverage of measured travel times of the sample dataτ̄ may or may not reflect an accurate measure ofthe actual population meanµ (absolutely every travel time that existed). The actual travel time mean canbe estimated using t distribution (since actual population variance is unknown) with a certain confidenceinterval 4

1 − α = 90%

t =τ̄ − µ

σ/√

n

The 90th percentile:

Pr(τ̄ − tα/2

σ√

n< µ < τ̄ + tα/2

σ√

n) = 0.9

(4)

whereτ̄ : Average travel time for the given data setσ : Standard deviation of travel times for the given data set

Reliability as a measure of non-failuresOne can perceive travel time reliability, R, as the probability of success of acertain route. This methodprovides probability of the extremes, pass or fail, defined in Equation 6. Success can take various meanings;in terms of travel time, a highway segment success can be defined as whether the actual travel time is belowor above a desired travel timeτd defined in Equation 5.

τd = τff + τth (5)

Ri =ST

N(6)

whereτd : Desired Travel Timeτff : Free Flow Travel Timeτth : Travel Time Threshold, ex: 5 minN : Sample sizeST : Total number of successes, whereτ < τd

Using this method, reliability of a highway segmentRs that consists of multiple contagious seg-mentsR1, R2 . . .Rn is determined as implied by Equation 7 (5)

Rs =n

∏

i=1

Ri (7)


Information Theory Based ApproachIn information theory, the information content, H(n), contained in a certain massage is given by Equation 8(11)

H(n) =n

∑

i=1

−Pilog2Pi

Pi = ni/n

n =k

∑

i=1

ni

(8)

whereH(n) : Information Contentn : Total number of various travel timesni : Frequency of travel times that lie within a specified interval

In terms of travel times, high information content indicates high variability on the considered seg-ment of the highway. Therefore, an inverse relation of the information content would be a reasonablemeasure of reliability. Such relation is given by Equation 9

R = 1/H(x) (9)

TRAVEL TIMES AND RELIABILITY ON THE I-15 LAS VEGAS

FIGURE 1 DMS on the I-15 corridor in Las Vegas from FAST

Dynamic Massage SignsThe travel time data was obtained from The Freeway Arterial System of Transportation (FAST), an inte-grated Intelligent Transportation System organization in the Las Vegas area. FAST has approximately 21Dynamic Massage Signs (DMS) mostly distributed along the I-15 as depicted in Figure 1. Travel timesare computed through the Incident Processing Module (IPM) in the Freeway Management System (FMS)where it processes detector data from traffic detector stations on the freeways; then, displayed on the DMS(7) (6).


Data ProcessingInitially, the dynamic message sign data received is a compilation of the date, time, location of the signidentifiers, the end destination, and the time traveled between segments along theI-15. The data record is incomma separated value format where each line of data is text.

Processing of the data is necessary to filter out some of the extraneous information in the data record andalso to reorganize the important elements such as the date, time, travel time, the sign identifier, and end des-tination. For the filtering process and data reorganization, code was writtenin visual basic for applications(VBA) to automate the process in excel. The program separates the data intonew sheets by the sign iden-tifier and end destination. Within each of these sheets, the data is organized by date and quarter hour. Foreach quarter hour, the average is computed. Using a pivot table with the day and end destination assigned tothe row field ,the hour and quarter hour assigned to the column field, and the average travel time assigned tothe data field, the data is reorganized into a new table where the averages are computed for each hour whilestill displaying the quarter hour averages.

Sign identifiers 13 and 17 were selected for analysis because they are located in main thoroughfares that arefrequently traversed. Sign identifier 17 is located on the southbound I-15freeway and it records the traveltime to the I-15. Sign identifier 13 is located on the northbound I-215 and it records the travel time to LakeMead parkway. By providing estimated travel times with a high degree of reliability, drivers will be able toplan their trips with greater ease and accuracy. Table (1(a)) contains a sample of the processed data. Afterthe data is processed, averages are computed for two hour intervals andfor days of the week as shown intables (1(b)) and (1(c)). Averaging the data for every two hour interval, allowed for analysis of consistencyof travel time between different periods of the day. Averaging the data for days of the week, allows foranalysis on a broader scope. Moreover, the consistency of the traveltime between days of the week can beassessed allowing for an efficient reliability measurement.

RESULTS AND DISSCUSSIONThe study was conducted for both analysis day-to-day variability and within-day variability using the fiveproposed methods.

Variability, Based on Normalized Standard Deviation (NSTD)A year worth of data was used to compile the averages. Tables 2(a) and 2(b) list the obtained NSTD for bothsigns.

Figures 2(a) and 4(a) show the normalized standard deviation trends forsigns 13 and 17.

Clearly, the results show higher variability in sign 13, north bound direction of the I15, from dayto day; yet interestingly, lower overall NTSD was obtained for within the dayanalysis compared to sign 17(I-15 south bound). Moreover, variability decreases for sign 13 during weekends and increases for sign 17.This phenomenon may be caused by the fact that driver’s destination forthat section of the freeway is mostlikely to be in the south direction during weekends since it leads to the center ofthe town. Overall reliabilityis not very high which means that traffic conditions on that segment are somewhat inconsistent Overallreliability is not very high which means that traffic conditions on that segment are somewhat consistant

Analysis of Variance ANOVATables 3(a), 3(b), 3(c), and 3(d) show theF value obtained from the ANOVA hypothesis test withα = 0.05.TheF values obtained from ANOVA analysis for both signs and the two types of analysis (day to day andwithin the day) are greater than the critical valueFα which indicates rejection of the null hypothesis. These


TABLE 1 Data Description(a) Processed Data

(b) Day to Day Averages

(c) Averages for two hour intervals

results show low consistency in travel times for the studied freeway section;thus, low reliability.

Average Travel Time EstimationTables 4(a) and 4(b) illustrate the average travel time with 95 percent confidence. Depicted in Figures 3(a)and 3(b)the 95th percentile for both signs.

As expected, the 95 th percentile averages approximately 18 and 14 minutes for sign 13 and 17,respectively during week days; however, it is much lower on weekends. Analyzing within the day values, itis noticeable that travel times are much higher in the afternoon than it is in the mornings as shown in Figures


TABLE 2 Normalized Standard Deviation(a) Day to day

(b) Within the day

(a) Day to Day (b) Within the Day

FIGURE 2 Normalized Standard Deviation Analysis

3(a) and 3(b).

Reliability as a Measure of Non-failuresTables 5(a), 5(b), 5(c), and 5(d) show the results obtained when non-failure analysis is used in determiningreliability. Figures 4(b) and 4(a) illustrate the trend for both day to day and within the day.

Data was compared to an eleven minute threshold based on a free flow speedof 65 mph as well assegment length which is approximately 10.5 and 7.7 miles for signs 13 and 14, respectively. The resultsshow a higher overall reliability for sign 17 (south bound) than it is for sign13 (north bound). The studiedfreeway section is unreliable in the afternoon as well as weekends for both directions. In this case reiabilityindicates whether travel times are above or below the desired travel time.

Information Theory Based ApproachThe reliability values obtained by using information theory are presented in Tables 6(a) and 6(b). The trendsof the reliability are depicted in Figures 5(a) and 5(b)

Conducting the analysis using information theory, results have demonstratedconsistency with thevalues obtained for NSTD showing higher reliability thereby lower variability for sign 17 (south bound)compared to sign 13 (north bound) during week days. A revered effect is seen when day is analyzed within


TABLE 3 Anaysis of Variance (ANOVA)(a) Sign 13, Day to day

(b) Sign 17, Day to day

(c) Sign 13, within the Day

(d) Sign 17, within the day

TABLE 4 Average travel time estimation with 95% confidence(a) Day to day

(b) Within the day

the day.


(a) Day to Day

(b) Within the Day

FIGURE 3 The 95th percentile


FIGURE 4 Reliability as non-failure Analysis


FIGURE 5 Information theory based reliability

CONCLUSIONSIn this study five reliability approaches were introduced, variability based on normalized standard deviation,analysis of Variance ANOVA, travel time mean estimation, reliability as a measure of non-failures, and


TABLE 5 Reliability as a measure of non-failure analysis(a) Sign 13, Day to day

(b) Sign 17, Day to day

(c) Sign 13, within the Day

(d) Sign 17, within the day

information theory based approach. These methos were applied to the I-15corridor in Las Vegas. Traditionalreliability measures were solely based on consistency. However, it does not address the issue of whetherthe travel time is acceptable or not regardless of its consistency. Put in other terms, consistency of traveltimes does not necessarily indicate desired travel times. Therefore, reliability measure based on non-failuresconsiders various thresholds when determining reliability. It was also demonstrated that reliability could beobtained based on information theory which analyzes the frequency of data belonging to certain intervals.


TABLE 6 Information Theory Based Reliaility(a) Day to day

(b) Within the day

REFERENCES[1] I.G. Black and J.G. Towriss. Demand Effects of Travel Time Reliability.Final report prepared for

London assessment division. UK Department of transport, 1993.

[2] Enide A.I. Bogers, Hans WC Van Lint, and HENK J Van Zuylen. Travel Time Reliability: EffectiveMeasures from a Behavioral Point of View.Transportation Research Board, page 1̋U14, 2008.

[3] Chao Chen, Alexander Skabardonis, and Pravin Varaiya. Travel-Time Reliability as a Measure of Ser-vice. Transportation Research Record: Journal of the Transportation Research Board, (1855):74̋U79,2003.

[4] Cambridge Systematics Inc. Traffic Congestion and Reliability Trends and Advanced Strategies forCongestion Mitigation.Prepared for Federal Highway Administration, page 140, 2005.

[5] Richard A. Johnson.Miller and Freund’s Probability and Statistics for Engineers. Prentice Hall, 1994.

[6] Kimley-Hom and Associates. FreewayManagement System Operator Manual. Prepared for NevadaDepartment of Transportation, (092202006), 2004.

[7] Kimley-Hom and Associates. FreewayManagement System Software Manual. Prepared for NevadaDepartment of Transportation, (092202006), 2004.

[8] J.W.C. Van Lint and H.J. Van Zuylen. Monitoring and Predicting Freeway Travel Time Reliability.Transportation Research Record, (1917):54–62, 2005.

[9] Yu Nie and Yueyue Fan. Arriving-on-Time Problem, Discrete Algorithm that Ensures Convergence.Transportation Research Record: Journal of the Transportation Research Board, (1964):193̋U200,2006.


[10] Jun-Seok Oh and Younshik Chung. Calculation of Travel Time Variability from Loop Detector Data.Transportation Research Record: Journal of the Transportation Research Board, (1945):12̋U23, 2006.

[11] Gordon Raisbeck.Information Theory. The MIT Press, 1964.

[12] Lam S.H., M. Jing, and A.A. Memon. Effects of Real-Time Information onRoute Choice Behavior:New Modeling Framework and Simulation Study in Behavioral Responses to ITS. Eindhoven, 2003.

[13] Ronald E. Walpole.Introduction to Statistics. Macmillan Publications, 1968.

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