TRAVEL TIME STANDARD SCORE AS A NEW MEASURE OF TRAVEL TIME

TRAVEL TIME STANDARD SCORE AS A NEW MEASURE OF TRAVEL 1

TIME RELIABILITY 2

3

4

5

Rui Wang 6

Department of Civil Engineering 7

Yokohama National University 8

79-5 Tokiwadai, Hodogaya, Yokohama 240-8501, Japan 9

Tel: +81-45-339-4039 10

[email protected] 11

12

13

Hiroshi Warita 14

Planning and Environment Department 15

Metropolitan Expressway Co.Ltd 16

1-4-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8930, Japan 17

Tel: +81-3-3539-9389 18


20

21

Masao Kuwahara 22

Institute of Industrial Science 23

University of Tokyo 24

4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan 25

Tel: +81-3-5452-6419 26


28

TRB 2010 Annual Meeting CD-ROM Paper revised from original submittal.

R. Wang, H. Warita and M. Kuwahara 1

ABSTRACT 1

In this paper, travel time standard score (TTSS) is proposed as a new measure of travel time 2

reliability. Here each single travel time data from an ETC (Electronic Toll Collection) system is 3

transferred to a TTSS value, based on the average and standard deviation of historical travel 4

times. Distributions of the TTSS at a certain time period are then used to evaluate the travel time 5

reliability performance. The result shows that TTSS distribution is more sensitive to the accident 6

happening situation than the traditional measures of travel time reliability, such like 95percentile 7

travel times. In addition, it has a potential to be used as a tool to better evaluate the influence of 8

travel time reliability experience on individual drivers’ future behavior. 9



INTRODUCTION 1

In this paper, we try to propose Travel Time Standard Score (TTSS) as a new measure of travel 2

time reliability, by utilizing data from Electronic Toll Collection (ETC) systems in Tokyo area. 3

4

Travel Time Reliability 5

Travel time reliability is defined as “a consistency or dependability in travel times, as measured 6

from day to day or across different times of day” (1). It is said to be a good measure of service of 7

expressway networks because it focuses more on unexpected delay caused by accidents or other 8

kinds of unexpected incidents (2)(3)(4). 9

The main purpose of travelers is to be sure to arrive at their destinations on time. Therefore, 10

compared with average travel time, travel time reliability often becomes a more important 11

concern of drivers. On the other hand, for the managing authorities of expressway road networks, 12

the travel time reliabilities of their network reflect their ability of incident management and can 13

give a different perspective in the evaluations of various improving works such as ITS solutions. 14

Currently the most widely used measures of travel time reliability are: 90th or 95

th percentile 15

travel times, buffer index, planning index, and so on (1). 16

17

About the ETC Data 18

After the adoption of an ETC system in 2001, usage of ETC is becoming more and more 19

common among drivers on the Tokyo Metropolitan Expressway Network (MEX). Currently 20

more than 80% of MEX’s 1.16 million daily drivers are using ETC to pay their toll (5). Similar 21

systems are rapidly widespread in the developing world as well, e.g. in Taiwan, Malaysia and 22

China. The entering and exiting records of the ETC using drivers consist of an important data 23

sources for various researches, after clearing the concerns of privacy protection. 24

In fact, vehicle detector data can also be used to estimate the common travel time reliability 25

measures (3)(4). However, vehicle detectors are usually poorly installed in developing countries. 26

With even poorer maintenance, the data can hardly be used in travel time related estimations (6). 27

Therefore the much more reliable ETC systems (as they must be) should have an important 28

potential in travel time related researches in developing countries as well (7). 29

30

Why TTSS is proposed? 31

Most of the traditional measures of travel time reliability, such like 90th or 95

th percentile travel 32

times, buffer index, planning index, are proved to be useful and successfully. They are capable of 33

providing some of the most important information that is related to travel time reliability. 34

However, these measures are sometimes difficult to be understood by normal drivers who 35

are not familiar with the traffic engineering terminologies. And all of them are aggregated 36



measures by paying more attention to the total general picture instead of the real experience of 1

the single drivers. 2

In Japan, and also in other oriental countries, standard scores (SS) are used for university 3

entrance tests, which are sure to be one of the most important lifetime events of almost every 4

people. Ordinary people are familiar with the SS term. When they, especially the parents, try to 5

evaluate performance a certain class or school, much more attention is paid to how many 6

students in the class can get extra high standard scores (i.e. enough to elite universities) than the 7

average scores. 8

Therefore, we propose the concept of Travel Time Standard Score (TTSS) in this paper. For 9

a certain road section during a certain time period, the ratios of drivers with some extra high 10

TTSS (eg. 60) can be used as a measure of its travel time reliability. This measure is much easier 11

for ordinary people to understand (at least in Japan). More importantly, we can also track the 12

single drivers’ historical records of TTSS, which are helpful for categorizing drivers and for 13

evaluating influence of travel time reliability experiences on single drivers’ future behavior. 14

15

Contents of the Paper 16

In this paper, at first ETC data are used to estimate some common day to day travel time and 17

travel time reliability measures on part of Route No.4, which is a major route that connecting a 18

major Japanese intercity expressway to the downtown of Tokyo. Then the statistic relationship 19

between travel time reliability measures and accident happenings is estimated and compared. 20

Our research is intended to describe and justify the usage of TTSS as a travel time reliability 21

measure that can be used to evaluate the effects of expressway accident control. 22

23

STUDY ROUTE AND TIME PERIOD 24

A 10.27km long route that connecting Chuo Intercity Expressway and Gaien Exit at downtown 25

Tokyo is chose for the research. It is a major route used by drivers from west part of Japan to the 26

downtown Tokyo, as shown in Figure 1. This route consists of 17 sections of lengths varying 27

from 210m to 1030m (averagely 604.1m). 28

A one-month data set of July 2006 is chose as the research period. In addition to ETC data, 29

we also use data from vehicle detectors (double type), and accident happening and endurance 30

time data (at 5-min time step), on all of the 17 sections. 31

The route is selected for two reasons. Firstly, it has relatively high accident happening rate 32

because there is an infamous and dangerous horizontal curve near the end of the route. Secondly, 33

the traffic volume of the route is high. We can collect adequate amount of ETC data on the route 34

to carry on this research. 35

36



MEASURES USED IN THE PAPER 1

2

Travel Time Measures 3

Travel time measures include: median travel times (mTT) and average travel times (aTT). 4

5

N

TT

aTT

N

i

i∑== 1 (1) 6

7

Traditional Travel Time Reliability Measures 8

A wide range of travel time reliability measures have been recommended by earlier researchers 9

(1) (2) (4). The following measures are used in this paper: 95th percentile travel times (95per TT), 10

buffer time (BT), and average travel time deviations (aTTD). 11

12

� 95th percentile travel time (95per TT) 13

The simplest method to measure travel time reliability by estimating the worst delays happened during the 14

research period. 15

16

� Buffer Time (BT) 17

Extra time that travelers have to add to the average travel times so that they can guarantee 18

on-time arrival 95 percent of the time, 19

20

BT =95per TT – aTT (2) 21

22

� Average travel time deviations (aTTD) 23

This is a measure to show the variation of travel times, the smaller the higher travel time 24

reliability, 25

N

aTTTT

aTTD

N

i

i∑=

−

= 1 (3) 26

27

where TTi is the travel time of the ith vehicle, and N is the total number of cars in the time period. 28

29

Travel Time Standard Score (TTSSi) of the ith vehicle 30

In this paper, we propose to use Travel Time Standard Score as a measure of travel time 31

reliability. Different from average travel times, we want to know more information about the 32



most extreme situations, such as travel times during congestions caused by accidents. In such 1

situations, TTSS should be a more convenient measure. We can easily find what a percentage of 2

travelers may have experienced some unusual (with higher standard deviations) travel times, by 3

using TTSS.. 4

5

5010 +⋅−

=aTTD

aTTTTTTSS i

i (4) 6

7

Just like to compare the performance of two classes in a high school, sometimes we have 8

more interest on the information of how many “excellent” students with outstanding standard 9

scores in each class. In equation (4), TTSS is adjusted to the same scale as scholastic test scores. 10

We propose to use the ratio of TTSS above 60 or 70 as a measure of travel time reliability in our 11

following research. One of the reasons is, in Japan, standard score of 60 is enough to get a 12

student to a top10 engineering school, and score of 70 would be no problem to even the 13

University of Tokyo. 14

15

Measure of Accident Happenings – NAP 16

In this paper, we use Number of accident congestion Affected time Periods (NAP) as a measure of 17

accident happening situations. NAP equals to the total number of 5-min time steps of sections 18

experiencing congestions caused by accidents. The NAP measure is chose because it shows both 19

the frequencies of accidents and their seriousness, because the measure gives both temporal and 20

spatial impacts of the congestions caused by the accidents. For a certain day, NAP is between 0 21

and the maximum value of 1020 (60×17), when all the 17 sections are experiencing accidents 22

through all the 60 time steps of 5 minutes in a 5-hour morning peak (6:00am ~ 11:00am). 23

24

∑=

=M

j

jSectionofStepsTimeAffectedofNumberNAP1

(5) 25

26

where M is the total number of sections on the research route. M =17, in this paper. 27

28

ESTIMATION RESULTS AND THE ANALYSIS 29

Here the daily average travel times, and the common travel time reliability measures of the study 30

route are estimated for all the workdays within the one month study period of July, 2006 at first. 31

Then analysis is carried on to describe the relationship between travel time reliability and 32

accident happenings. The data from July 13, 2006 are excluded because some technical errors 33

happened on that day. 34



Estimation Results – Common Measures of Travel Time and Travel Time Reliability 1

From the Table 1, we can see the daily average travel times and travel time reliability measures 2

of the morning peak hours (6:00 ~ 11:00) of all the workdays in July, 2006. 3

4

Estimation Results – Travel Time Standard Scores (TTSS) 5

By Equation (4), the TTSS of all single ETC travel times are calculated. Separated for days with, 6

or without accidents, Table 2 gives a summary of the average TTSS, the ratio of TTSS above 60, 7

and the ratio of TTSS above 70. We can find that although the average TTSS is not very different 8

between days with or without accidents (52.8 to 58.9), the average ratios of TTSS above 60 9

(26.4% to 40.6%) and 70 are totally different (11.1% to 23.1%). The comparison is more clearly 10

shown in Figure 3. 11

In Figure 4, we give out the distribution of TTSS scores. Our results show that for days with 12

accidents, the distribution of TTSS is wider, especially at the right part for the most extreme 13

values. Significant differences between the days with/without accidents can be found from the 14

TTSS of 60. 15

16

Relationship between Travel Time Reliability Measures and Accident Happenings 17

As shown in both Table 1 and Figure 2, obviously the measures of travel time reliability show much more 18

significant correlations with NAP, a measure of accident happenings used in this paper. All earlier authors 19

(1)(3)(4) mentioned the practical fact that, unlike average travel times, travel time reliabilities are more 20

dependent on the control of non-recurrent congestions, often caused by accidents and/or other incidents. 21

22

� Recurrent Congestions (by over demand) � average travel time 23

� Non-recurrent Congestions (by accidents, etc.) � travel time reliability 24

25

Our results give out a simple explanation of the above fact. All of the 3 travel time reliability 26

measures, 95per TT, BT, and aTTD show much higher correlations with NAP, if compared with aTT and 27

mTT. Especially for the measure of BT, where the average travel time aTT is subtracted, the highest 28

correlation with the accident happenings is found. 29

Furthermore, our research shows that we can use percentage of TTSS above 60 as a new 30

measure of travel time reliability. This measure can give out a clear picture of the higher travel 31

time deviations, as the result of non-recurrent congestions. Also it can be more easily understood, 32

at least in the Japanese context. 33

34

Comparison of the Major Measures of Travel Time Reliability 35

All of the major measures of travel time reliability are concerned with the variability of travel 36



times, but each is measuring a different aspect of the variability. 95 percentile travel times tell the 1

drivers what are the worst situations and can help them to make their travel plans. On the other 2

hand, aTTD is a more general measure of travel time variability as it measures the average 3

variation of travel times directly. However, aTTD is maybe also the most difficult measure for a 4

common driver to understand. 5

The TTSS measure pays more attention to the personal experience of the single drivers. 6

The drivers can have a very clear idea of what he has experienced: it was a normal situation, bad 7

situation, or extremely bad situation. Mainly in this sense, the TTSS measure is different from all 8

the current measures of travel time reliability. It is a personal experience of a driver, rather than a 9

mere statistic data of a road section. 10

11

CONCLUDING REMARKS 12

In the earlier works and in the practical world as well, travel time reliability measures are widely 13

used to show the effects of accident controls. In this paper, ETC data are used to analyze the 14

relationship between travel time reliability and accident happenings. We find that compared with 15

average travel times, travel time reliability measures show much higher correlations with 16

accident happenings, thus justify the usage of travel time reliability as an LOS measure of road 17

network. 18

In this paper, we discuss and prove the possibility of using Travel Time Standard Score 19

(TTSS) as a new measure of travel time reliability. TTSS is not only easier for the ordinary people 20

to understand (in Japan at least), the number of extra TTSS in a certain time period is proved to 21

be more sensitive to the accident happenings. Furthermore, more and more researchers are now 22

trying to analyze the influence of travel time reliability on drivers’ future behavior (8). By ETC 23

data, we can obtain long term historical records travel time reliability experience of single 24

drivers, which can be applied in this field. It is one of the authors’ main future directions. 25



ACKNOWLEDGMENTS 1

Most of the research was carried on in the Kuwahara Lab., Institute of Industrial Science, the 2

University of Tokyo. The authors would like to convey sincere appreciations to Metropolitan 3

Expressway (MEX) Co. Ltd. for providing valuable data for this study. The kindly suggestions 4

and encouragement from Prof. Nakamura, Prof. Okamura and other members of the 5

transportation lab at Yokohama National University are also highly appreciated. 6



REFERENCES 1

1. FHWA Publication, Travel time reliability: making it there on time, all the time, Federal 2

Highway Administration (FHWA), 2006. 3

4

2. Chen C., et al.: Travel time reliability as a measure of service, TRB 82nd Annual Meeting, 5

Washington D.C., 2003. 6

7

3. Maruyama, T., et al.: A study about the effect validation method of ITS by the travel time 8

reliability, Proceedings of the 6th ITS Symposium, pp. 361-366, 2007 9

10

4. Mehran, B. and Nakamura, H., Methodology for Assessing Impacts of Congestion Relief 11

Schemes on Travel Time Reliability, TRB 88th Annual Meeting, Washington D.C., 2009 12

13

5. MEX: http://www.shutoko.jp/company/press/h19/080128/index.html, official site of 14

Metropolitan Expressway (MEX), 2008. 15

16

6. Wang, R., et al.: Validation of an improved method to estimate expressway travel time by 17

the combination of detector and probe data, Journal of Eastern Asia Society for 18

Transportation Studies, Vol.4, pp.2003-2014, 2003. 19

20

7. Wang, R., et al.: Travel Time Reliability Analysis by ETC Data, Paper to be presented at the 21

39th Annual Spring Conference by the Infrastructure Planning Committee, Japan Society of 22

Civil Engineers, Tokushima, Japan, 2009. 23

24

8. Bogers, E., et al.: Reliability of Travel Time: Effective Measures from a Behavioral Point of 25

View, Transportation Research Record, Vol.2082, pp.27-34, 2008 26



LIST OF TABLES 1

Table 1 Estimation Results – Chuo Expressway to Gaien Exit, MEX (July, 2006)…………......11 2

Table 2 Comparison of TTSS, with or without accidents………………………………………..12 3

4

LIST OF FIGURES 5

Figure 1 Research Route…...……………………………………………………………………13 6

Figure 2 Comparison of Correlations with NAP………………………………………………...14 7

Figure 3 Comparison of TTSS, with or without accidents………………..……………………..15 8

Figure 4 Distributions of TTSS, with or without accidents……………………………………...169



TABLE 1 Estimation Results – Chuo Expressway to Gaien Exit, MEX (July, 2006) 1

aTT mTT 95per TT BT aTTDJul. 3(Mon.) 9.3 7.5 12.8 3.5 3.0 0Jul. 4(Tue) 16.4 15.1 28.7 12.3 5.6 95Jul. 5(Wed) 8.2 7.4 9.2 1.0 1.7 0Jul. 6(Thu) 14.1 14.1 18.8 4.7 3.6 0Jul. 7(Fri) 15.9 15.9 26.6 10.8 5.0 62Jul. 10(Mon) 10.6 9.1 14.4 3.8 3.2 0Jul. 11(Tue) 17.2 17.6 25.6 8.4 5.6 0Jul. 12(Wed) 18.8 19.2 36.4 17.6 6.4 0Jul. 14(Fri) 20.0 21.2 28.0 8.1 5.1 17Jul. 18(Tue) 16.8 15.8 27.4 10.6 2.8 85Jul. 19(Wed) 15.3 15.3 20.9 5.6 3.5 0Jul. 20(Thu) 15.4 14.2 31.7 16.3 5.5 117Jul. 21(Fri) 16.0 16.4 20.3 4.4 3.5 0Jul. 24(Mon) 16.2 14.4 39.1 22.9 5.5 36Jul. 25(Tue) 13.6 14.0 18.0 4.3 3.6 0Jul. 26(Wed) 19.4 18.9 32.4 13.0 6.1 0Jul. 27(Thu) 18.7 18.2 29.7 11.0 5.5 0Jul. 28(Fri) 19.0 17.9 33.3 14.3 5.5 0Jul. 31(Mon) 15.7 16.3 21.1 5.5 3.3 0Average 15.6 15.2 25.0 9.4 4.4 21.7Correlation with NAP 0.114 0.018 0.355 0.441 0.198

Average Travel TimesTravel Time Reliability MeasuresNAP

2



TABLE 2 Comparison of TTSS, with or without accidents 1

Average TTSS 1 2 3 4 5 6 7 8 9 10 11 12 13 MeanWithout Acc. 55.2 33.6 46.7 53.8 53.6 57.2 49.2 50.8 45.6 58.6 56.9 57.7 67.5 52.8With Acc. 51.8 50.6 59.8 88.1 49.5 53.8 58.9

Above 60 ratio (%) 1 2 3 4 5 6 7 8 9 10 11 12 13 MeanWithout Acc. 31.8 1.9 2.2 26.7 32.5 41.7 7.0 5.3 2.2 44.4 34.0 36.8 76.2 26.4With Acc. 26.7 18.1 60.7 86.1 17.5 34.7 40.6

Above 70 ratio (%) 1 2 3 4 5 6 7 8 9 10 11 12 13 MeanWithout Acc. 1.4 1.5 1.6 1.7 2.0 2.1 2.4 10.3 10.9 18.7 19.8 22.6 48.7 11.1With Acc. 8.5 10.9 12.6 13.3 20.3 72.8 23.1 2



1

FIGURE 1 Research Route 2

Chuo Exp.

Gaien



Comparison of Correlations with NAP

0.114

0.018

0.355

0.441

0.198

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

aTT mTT 95per TT BT aTTD

aTT

mTT

95per TT

BT

aTTD

1

FIGURE 2 Comparison of Correlations with NAP 2



Average TTSS

Above 60

Above 70

1.00 1.20 1.40 1.60 1.80 2.00 2.20

With /Without Acc. 1.12 1.54 2.09

Average TTSS Above 60 Above 70

1

FIGURE 3 Comparison of TTSS, with or without accidents 2



1

2

FIGURE 4 Distributions of TTSS, with or without accidents 3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 10 20 30 40 50 60 70 80 90 100

TTSS

Fre

quencie

sWith Acc.

Without Acc.


TRAVEL TIME STANDARD SCORE AS A NEW MEASURE OF TRAVEL TIME

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