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Estimation of Travel Time Values for Urban Public Transport Passengers Based on SP Survey
JOURNAL OF TRANSPORTATION SYSTEMS ENGINEERING AND INFORMATION TECHNOLOGY Volume 11, Issue 4, August 2011 Online English edition of the Chinese language journal RESEARCH PAPER
Cite this article as: J Transpn Sys Eng & IT, 2011, 11(4), 77í84.
Estimation of Travel Time Values for Urban Public Transport Passengers Based on SP Survey CHEN Xumei1,*, LIU Qiaoxian1, DU Guang2 1. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China 2. WISDRI Engineering & Research Incorporation Limited, Wuhan 430080, China
Abstract: Quantitative study on the travel costs of urban transit passengers has great significance for scientifically evaluating social benefits of public transportation system. Analysis of travel time values is one of the most important parts of traveler’s travel cost estimation. According to the stated preference (SP) survey data for Beijing residents, factors that influence public transport values of travel time are analyzed and a Logit-based model is used. An improved SP survey based model is proposed, in which traveler’s income is introduced as a variable. The parameters estimating the travel time values under the trip purposes of work/business and leisure are calibrated. Then the values of travel time under different conditions in Beijing are obtained (i.e. different trip purposes and with/without transferring). The results indicate that the travel time values for work are generally higher than those for leisure. The waiting time values are higher than transferring time values and in-vehicle time values under any circumstances, and the waiting time values are higher with transferring than those without transferring. Key Words: urban traffic; public transit; stated preference (SP) survey; travel time value; scenario design
1
Introduction
Travel time value analysis plays an important role in the economic benefit evaluation of transportation projects. Travel time savings are the principal benefit of public transport investment projects that can be quantified. However, there are different perceptions of travel time values for different regions, eras and trip purposes[1]. The research on travel time values for public transport system is one of the most important and difficult tasks. Many studies on travel time values have been conducted recently by domestic and international scholars. After a review of the literature in China and foreign countries, three widely used methods to calculate travel time values emerged. They are the product method, the income method and the willingness-to-pay method, which are based on the Probit model or the Logit model[2,3]. Nowadays, Stated Preference (SP) survey has been used extensively in the field of transportation because of its capability to make good use of data, its high efficiency and its low cost[4]. For example, Wang[5] discussed the definition of travel time value and its
influencing factors in depth. He established a simplified travel time value model for Beijing residents. SP survey was adopted to collect data and calibrate model parameters. The travel time values for residents in Beijing were obtained. Fu et al[6]. quantified the travel time values of Beijing residents with a simplified Multinomial Logit (MNL) model. The time values of urban public transport system in Beijing were calculated based on an analysis of transit travelers characteristics. Travel time, travel cost, income and other factors were also considered. Hess et al. [7] discussed some of the issues that arose with the computation of the implied values of traveltime savings in the case of discrete choice models allowing for random taste heterogeneity. The coefficients of Multinomial Logit (MNL) and Mixed Multinomial Logit (MMNL) models for travel time values estimation were calculated, and distributions of travel time values were presented. Steimetz and Brownstone[8] applied the multiple imputation method to estimate the travel time values of commuters (full-time workers and part-time workers), which varied with trip distance. In general, progress has been made in the studies of travel
Received date: Apr 12, 2011; Revised date: May 6, 2011; Accepted date: May 12, 2011 *Corresponding author. E-mail: [email protected] Copyright © 2010, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(10)60132-8
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
time valuations after many years of research. However, the existing studies concentrate on the relationship between travel time values and costs rather than on the income. The impact of the travel process of transit travelers on estimating travel time values has not been analyzed in detail. To this end, the Logit model has been chosen as a basic model in this paper and traveler’s income is introduced as a new variable. The number of transfers is also considered to estimate the waiting time values, in-vehicle time values and transferring time values under different trip purposes.
2
Data collection in SP survey
2.1 SP questionnaire design In the SP survey, the correlation among different factors is relatively low, so it is possible to get several data from each respondent. As a result, we can make good use of the surveyed data. The questionnaire is designed according to the following four principles: ķTrips include work/business purpose and leisure purpose.
ĸ Basic information of respondents includes sex and income. Income is divided into five groups (1-1200, 1201-3000, 3001-6000, 6001-10000, ˚ 10000 Yuan per month). ĹThe questionnaire type is designed with a transferring vs. without transferring scenarios. The with transferring scenarios are further divided into four types; transferring from bus to bus/subway with one-transfer trip, transferring from rail to bus/subway with one-transfer trip, transferring from bus to bus/subway with two-transfer trip and transferring from rail to bus/subway with two-transfer trip. ĺWhen designing the scenarios for trips using a public transport system, typical statistics on trips for residents in Beijing should be analyzed. Thus, the range of travel costs and times can be obtained. These travel costs and times are categorized into 6 scenarios using a uniform design[5] method, which are designed to investigate the differences between the with transferring and without transferring scenarios, as shown in Tables 1 through 5.
Table 1 Without transferring scenario Bus (without transferring)
Subway (without transferring)
Total time
Waiting time
In-vehicle time
Fare
Total time
Waiting time
In-vehicle time
Fare
23
9
14
0.8
11
2
9
2
38
10
28
1.5
21
3
18
2
49
11
38
0.4
32
5
27
2
25
13
12
1.2
11
6
5
2
39
16
23
0.2
21
8
13
2
55
18
37
1
33
9
24
2
Table 2 Scenario of Transferring from Bus to Bus/Subway with One-transfer Trip Bus to Bus (one transfer) Total time
Transferring time
34 56
Bus to Subway (one transfer)
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
1
7
26
1.5
19
2
3
14
2
4
13
39
1.2
37
5
5
27
2
39
5
14
20
1
22
6
8
8
2
48
5
6
37
0.8
32
7
3
22
2
34
6
11
17
0.4
19
8
4
7
2
46
6
13
27
0.2
32
9
7
16
2
Table 3 Scenario of Transferring from Rail to Bus/Subway with One-transfer Trip Rail to Bus (one transfer)
Rail to Subway (one transfer)
Total time
Transferring time
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
35
2
9
24
1.5
21
1
3
17
2
58
6
15
37
1.2
37
4
6
27
2
42
6
19
17
1
22
5
8
9
2
53
9
8
36
0.8
34
6
3
25
2
35
8
12
15
0.4
20
7
5
8
2
57
10
18
29
0.2
35
8
8
19
2
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
Table 4 Scenario of Transferring from Bus to Bus/Subway with Two-transfer Trip Bus to Bus (two transfer) Total time
Transferring time
33 54
Bus to Subway (two transfer)
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
1
8
24
1.5
21
2
3
16
2
4
12
38
1.2
41
6
6
29
2
38
5
15
18
1
25
6
9
10
2
48
5
7
36
0.8
34
6
2
26
2
33
6
11
16
0.4
19
7
4
8
2
48
6
13
29
0.2
33
8
7
18
2
Table 5 Scenario of Transferring from Rail to Bus/Subway with Two-transfer Trip Rail to Bus (two transfer) Total time
Transferring time
34 58 40
Rail to Subway (two transfer)
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
3
8
23
1.5
20
1
3
16
2
6
14
38
1.2
39
5
6
28
2
6
18
16
1
24
5
9
10
2
52
9
8
35
0.8
34
6
2
26
2
37
8
13
16
0.4
19
7
5
7
2
54
9
18
27
0.2
34
7
8
19
2
Note: The unit of time is minutes while the unit of fare is Yuan in Tables 1 through 5.
2.2 SP survey and data checking Respondents of the SP survey were urban residents living in Beijing. They were interviewed from January to March 2010. Interviews were carried out at the Xidan Dayuecheng Shopping Mall, the Beijing Railway Station and the Huaxing International Cinema. A total of 2,307questionnaires were collected. Respondents chose different travel schemes from the six scenarios according to their own judgment. The questionnaires were randomly distributed to respondents in order to guarantee validity of the samples. SP survey has limitations because respondents may choose travel schemes according to their subjective judgment that are inconsistent with their real behavior. Therefore, the surveyed data should be processed and checked in order to reduce errors due to this inconsistency.[9] A total of 1,768 valid samples, which corresponded to 10,608 datasets, were obtained after eliminating the subjective and illogical data. The effective data accounted for 76.6% of the total data. 2.3 Preliminary analysis of data from SP survey
(1) Probability analysis Respondents chose travel schemes for each scenario based on the designated six scenarios in the questionnaire. Fuzzy mathematics is applied to transform ambiguous statements into quantified probability. The probability for “must choose the travel mode of bus or subway” is 95%, for “likely choose the travel mode of bus or subway” it is 75% and for “I don’t care to choose bus or subway” is 50%. (2) Income analysis for travelers The marginal utility of travel time increases with the increase in income. Collinearity[3] will occur if income is introduced into the utility model directly. The collinearity could be eliminated if the median of income ranges is introduced. In addition, because respondents whose income is higher than 10,000 Yuan/month must choose subway in this survey, their data should be removed because they do not care about the difference in travel time or the cost between the bus and the subway. Table 6 shows the final income ranges and the medians.
Table 6 Distribution of Income Range Income range(Yuan/month)
0I1200
1201I3000
3001I6000
6001I10000
Median
600
2100.5
4500.5
8000.5
3 Travel time values model for public transport system and parameters calibration 3.1 Model establishment (1) Basic model analysis According to the literature review on travel time
valuation, the product method and income method deviate from the willingness-to-pay principle since mental pain (such as fatigue or anxiety) due to travel time delay cannot be considered. Therefore, this paper uses the willingness-to-pay principle and Logit model as the basis. Among all travel modes, travel time and cost are the most important factors that
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
influence choice of travel modes. Therefore, the utility model of the mode i is expressed as follows: Vi Įi ȕiCi ȖT (1) i i
Pi
k
exp Įi ȕiCi ȖiTi ¦ exp Įk ȕk Ck ȖkTk
exp Vi / ¦ e
Vj
j 1
(2)
M
where Vi is the utility function of the mode i; Ci is a cost variable of the mode i; Ti represents a travel time variable of the mode i; Įi ˈ ȕi and Ȗi are model parameters that need to be calibrated and Pi is the probability that travelers will choose the travel mode i. Let D D i D j , E Ei E j ˈ J J i J j ˈ 'Cij Ci C j and 'Tij Ti T j . Pi and Pj are the probabilities that travelers will choose the travel mode i or j . The travel time values model can be formulated as follows:
Ln
Pi Pj
Į ȕ'Cij Ȗ'Tij
(3)
VOT
(4)
Ȗ/ȕ
where VOT means the values of time. This basic model is commonly used to value travel time. Only travel time and cost are considered in this utility function. However, the actual situation is complex. In addition to travel time and cost, other factors, including trip purpose and income can influence the values of travel time greatly. (2) Model improvement The travel time of public transport systems consists of transferring time, waiting time and in-vehicle time, so the time variable Ti can be divided into transferring time T 1i , waiting time T 2 i and in-vehicle time T 3i . In the utility function Vi Įi ȕiCi ȖiTi , Vi decreases with the increase in the cost variable Ci , which changes Vi combined with E i . Vi also decreases with the increase in travel time Ti , which changes Vi combined with Ȗi . The income variable I q does not have a direct influence on Vi , but it can influence the degree for Ci to change Vi . That is to say, I q can influence ȕi . When travel time Ti is fixed and Ci changes 'Ci , the utility variation 'V1 with low income variable I q is greater than the utility variation 'V2 with high income variable I q . This means that travelers with low income are more sensitive to travel costs. Consequently, we can assume that the relation between I q and ȕi is as follows:
ȕi
Ȧi
Ȝi Iq
(5)
ȕi
Ȧi
Ȝi LnI q
(6)
ȕi
Ȧi
Ȝi I qș
(7)
Equation (8), (9) and (10) can be deduced as three different kinds of utility function when we substitute the three assumed ȕi expressed with equation (5), (6) and (7) in equation (1). Furthermore, according to equation (3) on the utility function,
we can get three kinds of utility functions with the added income variable.
Ȧi
When ȕi
Ȝi , Iq
the utility function can be expressed as
Ln
Pi Pj
Ȧi
When ȕi
Ȝi 'Cij Iq
(8)
Ȝi 'Cij Ln I q
(9)
Ȝi 'Cij I qș
(10)
Į Ȧi 'Cij Ȗ'Tij Ȝi , Ln I q
the utility function can be expressed as
Ln
Pi Pj
When ȕi
Į Ȧi 'Cij Ȗ'Tij Ȧi
Ȝi , I qș
the utility function can be expressed as
Ln
Pi Pj
Į Ȧi 'Cij Ȗ'Tij
(3) Model optimization By analyzing the data from the SP survey using regression analysis, three VOT models, in which the income variable has the form of a polynomial, logarithmic or exponential expression, are improved and the optimal model is identified. The detailed steps are as follows: ķ The VOT model with a polynomial income variable is tested. After importing the preliminary processed data to SPSS software, we define variable names and use REGRESSION module in SPSS to output the regression equation and standard deviation of coefficients. ĸ We conduct the test of goodness of fit for the regression equation, the test of significance for regression parameters and the test of significance for the regression equation. Ĺ We repeat step ķ and ĸ and output the results when the VOT model has a logarithmic and exponential income variable. ĺ Different regression equations with three different income variable forms and test results are compared, as shown in Table 7. Ļ We compare these test results. The optimal model which has a logarithmic income variable is identified because it has the highest R and R 2 , the results of the test of significance for regression parameters are all lower than 0.05, and it has the best results of the test of significance for regression equation. Finally, the optimal VOT model is formulated as follows:
Ln Pi / Pj Į Ȧ'Cij Ȗ1'T 1ij Ȗ2 'T 2ij
Ȗ3'T 3ij Ȝ'Cij / Ln I q Ȗ1,2,3 VOT1,2,3 Ȧ Ȝ/LnI q
(11) (12)
where, Pi and Pj are the probabilities that traveler q will
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
choose the travel mode i or j and Pi Pj 1 ; VOT1 is transferring time values, VOT2 is waiting time values, and VOT3 is in-vehicle time values; 'Cij is the difference between the travel costs for the travel mode i and j, for which the unit of Yuan is used; 'T 1ij , 'T 2ij and 'T 3ij are the differences between two
transferring times, two waiting times and two in-vehicle times for the travel mode i and j, for which the unit of hour is used; I q is the income variable, for which the unit of Yuan/month is used; Į , Ȧ , Ȗ1 , Ȗ2 , Ȗ3 and Ȝ are parameters that needed to be calibrated.
Table 7 Summary of Test Results
Test of goodness of fit for regression equations
Polynomial
Logarithmic
Exponential
R2
0.845
0.851
0.850
R2
0.837
0.843
0.842
R
0.919
0.922
0.922
Value of Sig.
Value of Sig.
Value of Sig.
Constant
0.062
0.057
0.058
'C
0.000
0.000
0.213
'T1
0.014
0.013
0.013
'T2
0.000
0.000
0.000
'C / I q
0.000
——
——
'C / LnI q
——
0.000
——
'C / I qT
——
——
0.000
Test of significance for regression parameters
Test of significance for regression equations
Iq in models
Form of
Test items
T
——
——
0.000
Value of F
98.292
102.695
102.377
Value of p
0.000
0.000
0.000
3.2 Model parameters calibration The regression for data from the SP survey is performed with the SPSS software after the optimal VOT model is identified. The parameters necessary for the estimation of the
travel time values under the trip purposes of work/business and leisure, as well as with vs. without transferring are calibrated. The results are shown in Table 8.
Table 8 Model Parameters Calibration Parameters Trip purpose
Work/Business
Leisure
Į
Ȧ
Ȗ1
Ȗ2
Ȗ3
Ȝ
Without transferring
–1.48
0.035
—
–4.24
–3.78
–7.75
With transferring
–0.346
0.165
–2.46
–6.56
–4.18
–10.22
Without transferring
–1.61
-0.085
—
–3.44
–2.80
–6.93
With transferring
–0.48
0.071
–3.4
–6.06
–3.36
–8.88
3.3 Model results analysis After the parameters used to estimate the travel time values under the trip purposes of work/business and leisure are calibrated, the values of time for different trip purposes, with vs. without transferring, and different income levels are estimated according to equation (12). (1) Travel time values without transferring for work and business purpose When there is no transferring, the waiting time values and in-vehicle time values increase with the increase in income for work and business purposes (as illustrated in Fig. 1). The waiting time values are generally higher than in-vehicle time values. This demonstrates that travelers pay more attention to waiting time, and anxiety appears when travelers wait for the buses or subways.
(2) Travel time values with transferring for work and business purposes When travelers use transfer services (including transferring from bus with one-transfer trip, transferring from subway with one-transfer trip, transferring from bus with two-transfer trip or transferring from subway with two-transfer trip), the transferring time values, the waiting time values and the in-vehicle time values increase (as illustrated in Fig. 2) when the income of travelers whose trip purpose is work and business rises. Time spent waiting for bus or subway is more highly valued than in-vehicle time and transferring time, while the mean time, the transferring time values are lower than in-vehicle time values. (3) Travel time values without transferring for leisure purposes The waiting time values and in-vehicle time values (as
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
illustrated in Fig. 3) without transferring increase when income in the case of leisure purposes increases. The waiting :DLWLQJ7LPH9DOXHV
time values are higher than in-vehicle time values.
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Fig. 2 Travel Time Values with Transferring for Work and Business Purposes 7UDQVIHUULQJ7LPH9DOXHV
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Fig. 1 Travel Time Values without Transferring for Work and Business Purposes
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Fig. 3 Travel Time Values without Transferring for Leisure Purposes
(4) Travel time values with transferring for leisure purposes As travelers’ incomes rise, the value people place on transferring time, waiting time and in-vehicle time increases (as illustrated in Fig. 4) with travel (including transferring from bus with one-transfer trip, transferring from subway with one-transfer trip, transferring from bus with two-transfer trip and transferring from subway with two-transfer trip) for leisure purposes. The waiting time tends to be relatively higher than the time spent in-vehicle and transferring, while the transferring time values are almost the same as in-vehicle time values. In general, the travel time values for work and business purposes are higher than those for leisure purposes. This is because travelers must arrive at the destination on time when they have work and business trips. They feel increased time stress and are more sensitive to time than to cost. Therefore, time values for work and business purposes tend to be greater than time values for leisure purposes. This reflects the increased time stress for work and business purposes. The waiting time values are greater with transferring than those without transferring, no matter if they are for business purposes or for leisure purposes. This indicates that travelers feel more anxious when waiting for the bus or subway after transferring. The in-vehicle time values with transferring are
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Fig. 4 Travel Time Values with Transferring for Leisure Purposes
nearly equal to the time values without transferring. This is due to the fact that transferring has little impact on in-vehicle time values. The waiting time values are higher than transferring time values and in-vehicle time values for any purpose. This means that travelers have the highest anxiety level when waiting for the bus or subway.
4
Conclusions
SP survey is used to obtain travel behavior data from Beijing residents, and an improved time value model for the public transport systems was proposed in this paper. Moreover, the transferring time values, the waiting time values and the in-vehicle time values for various conditions in Beijing were obtained, which provide a support for the analysis of travel costs for the public transport system. The results indicate that time values for work purposes are generally higher than those for leisure purposes, and time values increase with the increase of travelers’ incomes. Meantime, waiting time values are higher than in-vehicle time values and transferring time values because travelers are more anxious when waiting than when in-vehicle or transferring. Transferring time is valued less than in-vehicle time for work and business purposes with transferring. This is because trips for work and business
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
purposes occur during peak hours with heavy traffic flow and crowded buses or subways. Travelers are more anxious when they are in-vehicle than when they are transferring from one vehicle to another because they feel uncomfortable because of crowded circumstances and traffic congestion. Transferring time values are nearly the same as in-vehicle time values for leisure purposes (such as shopping or entertainment) with transferring. Compared with the route for work and business purposes, the route and the transferring time for of leisure purposes are more flexible. At the same time, leisure trips typically occur during off-peak hours, and the vehicle is comfortable because it is less crowded. Furthermore, in-vehicle time values for work and business purposes are higher than those for leisure purposes, with or without transfer. Comfort in vehicle is one of the reasons for this, not to mention less time stress for leisure trips. The bus or subway is less crowed during off-peak hours because work and business trips occur at peak hours, while leisure trips take place during off-peak hours. The research on travel time values involves many areas, such as traffic engineering, economics and statistics. There are a great many factors affecting travel time values. Further studies can be carried out to analyze additional factors that may influence travel time values in the future.
Acknowledgements This work was supported by the National High Technology Research and Development Program of China(863 Program).
References [1]
Wang F. Study on behavior value of time based on stated preference survey. Beijing University of Technology, 2005.
[2] Wardman M. A review of British evidence on time and service quality valuations. Transportation Research Part E, 2001, 37: 107–128. [3] Bu C, Lin X Y. Study on improvement of Logit model for value of travel time. Technology Economics, 2009, 28(3): 62–65. [4] Du G. Study on travel time value of urban public transportation based on stated preference survey. Beijing Jiaotong University, 2009. [5] Wang F, Chen J C, Chen Y Y. Uniformity design method for SP survey in transportation. Urban Transport of China, 2005, 3(3): 69–72. [6] Fu W W, Jin W Z, Lin F C. Calculation of time value for urban public travel with MNL model. Journal of Transportation Systems Engineering and Information Technology, 2010, 10(2): 148–152. [7]
Hess S, Bierlarie M, Polak J W. Estimation of value of travel-time savings using mixed Logit models. Transportation Research Part A, 2005, 39: 221–236.
[8] Steimetz S S C, Brownstone D. Estimating commuters’ “value of time” with noisy data: A multiple imputation approach. Transportation Research Part B, 2005, 39: 865–889. [9] Wardman M. Stated preference methods and travel demand forecasting: an examination of the scale factor problem. Transportation Research Part A, 1991, 25(2): 79–89.
Cite this article as: J Transpn Sys Eng & IT, 2011, 11(4), 77í84.
Estimation of Travel Time Values for Urban Public Transport Passengers Based on SP Survey CHEN Xumei1,*, LIU Qiaoxian1, DU Guang2 1. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China 2. WISDRI Engineering & Research Incorporation Limited, Wuhan 430080, China
Abstract: Quantitative study on the travel costs of urban transit passengers has great significance for scientifically evaluating social benefits of public transportation system. Analysis of travel time values is one of the most important parts of traveler’s travel cost estimation. According to the stated preference (SP) survey data for Beijing residents, factors that influence public transport values of travel time are analyzed and a Logit-based model is used. An improved SP survey based model is proposed, in which traveler’s income is introduced as a variable. The parameters estimating the travel time values under the trip purposes of work/business and leisure are calibrated. Then the values of travel time under different conditions in Beijing are obtained (i.e. different trip purposes and with/without transferring). The results indicate that the travel time values for work are generally higher than those for leisure. The waiting time values are higher than transferring time values and in-vehicle time values under any circumstances, and the waiting time values are higher with transferring than those without transferring. Key Words: urban traffic; public transit; stated preference (SP) survey; travel time value; scenario design
1
Introduction
Travel time value analysis plays an important role in the economic benefit evaluation of transportation projects. Travel time savings are the principal benefit of public transport investment projects that can be quantified. However, there are different perceptions of travel time values for different regions, eras and trip purposes[1]. The research on travel time values for public transport system is one of the most important and difficult tasks. Many studies on travel time values have been conducted recently by domestic and international scholars. After a review of the literature in China and foreign countries, three widely used methods to calculate travel time values emerged. They are the product method, the income method and the willingness-to-pay method, which are based on the Probit model or the Logit model[2,3]. Nowadays, Stated Preference (SP) survey has been used extensively in the field of transportation because of its capability to make good use of data, its high efficiency and its low cost[4]. For example, Wang[5] discussed the definition of travel time value and its
influencing factors in depth. He established a simplified travel time value model for Beijing residents. SP survey was adopted to collect data and calibrate model parameters. The travel time values for residents in Beijing were obtained. Fu et al[6]. quantified the travel time values of Beijing residents with a simplified Multinomial Logit (MNL) model. The time values of urban public transport system in Beijing were calculated based on an analysis of transit travelers characteristics. Travel time, travel cost, income and other factors were also considered. Hess et al. [7] discussed some of the issues that arose with the computation of the implied values of traveltime savings in the case of discrete choice models allowing for random taste heterogeneity. The coefficients of Multinomial Logit (MNL) and Mixed Multinomial Logit (MMNL) models for travel time values estimation were calculated, and distributions of travel time values were presented. Steimetz and Brownstone[8] applied the multiple imputation method to estimate the travel time values of commuters (full-time workers and part-time workers), which varied with trip distance. In general, progress has been made in the studies of travel
Received date: Apr 12, 2011; Revised date: May 6, 2011; Accepted date: May 12, 2011 *Corresponding author. E-mail: [email protected] Copyright © 2010, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(10)60132-8
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
time valuations after many years of research. However, the existing studies concentrate on the relationship between travel time values and costs rather than on the income. The impact of the travel process of transit travelers on estimating travel time values has not been analyzed in detail. To this end, the Logit model has been chosen as a basic model in this paper and traveler’s income is introduced as a new variable. The number of transfers is also considered to estimate the waiting time values, in-vehicle time values and transferring time values under different trip purposes.
2
Data collection in SP survey
2.1 SP questionnaire design In the SP survey, the correlation among different factors is relatively low, so it is possible to get several data from each respondent. As a result, we can make good use of the surveyed data. The questionnaire is designed according to the following four principles: ķTrips include work/business purpose and leisure purpose.
ĸ Basic information of respondents includes sex and income. Income is divided into five groups (1-1200, 1201-3000, 3001-6000, 6001-10000, ˚ 10000 Yuan per month). ĹThe questionnaire type is designed with a transferring vs. without transferring scenarios. The with transferring scenarios are further divided into four types; transferring from bus to bus/subway with one-transfer trip, transferring from rail to bus/subway with one-transfer trip, transferring from bus to bus/subway with two-transfer trip and transferring from rail to bus/subway with two-transfer trip. ĺWhen designing the scenarios for trips using a public transport system, typical statistics on trips for residents in Beijing should be analyzed. Thus, the range of travel costs and times can be obtained. These travel costs and times are categorized into 6 scenarios using a uniform design[5] method, which are designed to investigate the differences between the with transferring and without transferring scenarios, as shown in Tables 1 through 5.
Table 1 Without transferring scenario Bus (without transferring)
Subway (without transferring)
Total time
Waiting time
In-vehicle time
Fare
Total time
Waiting time
In-vehicle time
Fare
23
9
14
0.8
11
2
9
2
38
10
28
1.5
21
3
18
2
49
11
38
0.4
32
5
27
2
25
13
12
1.2
11
6
5
2
39
16
23
0.2
21
8
13
2
55
18
37
1
33
9
24
2
Table 2 Scenario of Transferring from Bus to Bus/Subway with One-transfer Trip Bus to Bus (one transfer) Total time
Transferring time
34 56
Bus to Subway (one transfer)
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
1
7
26
1.5
19
2
3
14
2
4
13
39
1.2
37
5
5
27
2
39
5
14
20
1
22
6
8
8
2
48
5
6
37
0.8
32
7
3
22
2
34
6
11
17
0.4
19
8
4
7
2
46
6
13
27
0.2
32
9
7
16
2
Table 3 Scenario of Transferring from Rail to Bus/Subway with One-transfer Trip Rail to Bus (one transfer)
Rail to Subway (one transfer)
Total time
Transferring time
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
35
2
9
24
1.5
21
1
3
17
2
58
6
15
37
1.2
37
4
6
27
2
42
6
19
17
1
22
5
8
9
2
53
9
8
36
0.8
34
6
3
25
2
35
8
12
15
0.4
20
7
5
8
2
57
10
18
29
0.2
35
8
8
19
2
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
Table 4 Scenario of Transferring from Bus to Bus/Subway with Two-transfer Trip Bus to Bus (two transfer) Total time
Transferring time
33 54
Bus to Subway (two transfer)
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
1
8
24
1.5
21
2
3
16
2
4
12
38
1.2
41
6
6
29
2
38
5
15
18
1
25
6
9
10
2
48
5
7
36
0.8
34
6
2
26
2
33
6
11
16
0.4
19
7
4
8
2
48
6
13
29
0.2
33
8
7
18
2
Table 5 Scenario of Transferring from Rail to Bus/Subway with Two-transfer Trip Rail to Bus (two transfer) Total time
Transferring time
34 58 40
Rail to Subway (two transfer)
Waiting time
In-vehicle time
Fare
Total time
Transferring time
Waiting time
In-vehicle time
Fare
3
8
23
1.5
20
1
3
16
2
6
14
38
1.2
39
5
6
28
2
6
18
16
1
24
5
9
10
2
52
9
8
35
0.8
34
6
2
26
2
37
8
13
16
0.4
19
7
5
7
2
54
9
18
27
0.2
34
7
8
19
2
Note: The unit of time is minutes while the unit of fare is Yuan in Tables 1 through 5.
2.2 SP survey and data checking Respondents of the SP survey were urban residents living in Beijing. They were interviewed from January to March 2010. Interviews were carried out at the Xidan Dayuecheng Shopping Mall, the Beijing Railway Station and the Huaxing International Cinema. A total of 2,307questionnaires were collected. Respondents chose different travel schemes from the six scenarios according to their own judgment. The questionnaires were randomly distributed to respondents in order to guarantee validity of the samples. SP survey has limitations because respondents may choose travel schemes according to their subjective judgment that are inconsistent with their real behavior. Therefore, the surveyed data should be processed and checked in order to reduce errors due to this inconsistency.[9] A total of 1,768 valid samples, which corresponded to 10,608 datasets, were obtained after eliminating the subjective and illogical data. The effective data accounted for 76.6% of the total data. 2.3 Preliminary analysis of data from SP survey
(1) Probability analysis Respondents chose travel schemes for each scenario based on the designated six scenarios in the questionnaire. Fuzzy mathematics is applied to transform ambiguous statements into quantified probability. The probability for “must choose the travel mode of bus or subway” is 95%, for “likely choose the travel mode of bus or subway” it is 75% and for “I don’t care to choose bus or subway” is 50%. (2) Income analysis for travelers The marginal utility of travel time increases with the increase in income. Collinearity[3] will occur if income is introduced into the utility model directly. The collinearity could be eliminated if the median of income ranges is introduced. In addition, because respondents whose income is higher than 10,000 Yuan/month must choose subway in this survey, their data should be removed because they do not care about the difference in travel time or the cost between the bus and the subway. Table 6 shows the final income ranges and the medians.
Table 6 Distribution of Income Range Income range(Yuan/month)
0I1200
1201I3000
3001I6000
6001I10000
Median
600
2100.5
4500.5
8000.5
3 Travel time values model for public transport system and parameters calibration 3.1 Model establishment (1) Basic model analysis According to the literature review on travel time
valuation, the product method and income method deviate from the willingness-to-pay principle since mental pain (such as fatigue or anxiety) due to travel time delay cannot be considered. Therefore, this paper uses the willingness-to-pay principle and Logit model as the basis. Among all travel modes, travel time and cost are the most important factors that
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
influence choice of travel modes. Therefore, the utility model of the mode i is expressed as follows: Vi Įi ȕiCi ȖT (1) i i
Pi
k
exp Įi ȕiCi ȖiTi ¦ exp Įk ȕk Ck ȖkTk
exp Vi / ¦ e
Vj
j 1
(2)
M
where Vi is the utility function of the mode i; Ci is a cost variable of the mode i; Ti represents a travel time variable of the mode i; Įi ˈ ȕi and Ȗi are model parameters that need to be calibrated and Pi is the probability that travelers will choose the travel mode i. Let D D i D j , E Ei E j ˈ J J i J j ˈ 'Cij Ci C j and 'Tij Ti T j . Pi and Pj are the probabilities that travelers will choose the travel mode i or j . The travel time values model can be formulated as follows:
Ln
Pi Pj
Į ȕ'Cij Ȗ'Tij
(3)
VOT
(4)
Ȗ/ȕ
where VOT means the values of time. This basic model is commonly used to value travel time. Only travel time and cost are considered in this utility function. However, the actual situation is complex. In addition to travel time and cost, other factors, including trip purpose and income can influence the values of travel time greatly. (2) Model improvement The travel time of public transport systems consists of transferring time, waiting time and in-vehicle time, so the time variable Ti can be divided into transferring time T 1i , waiting time T 2 i and in-vehicle time T 3i . In the utility function Vi Įi ȕiCi ȖiTi , Vi decreases with the increase in the cost variable Ci , which changes Vi combined with E i . Vi also decreases with the increase in travel time Ti , which changes Vi combined with Ȗi . The income variable I q does not have a direct influence on Vi , but it can influence the degree for Ci to change Vi . That is to say, I q can influence ȕi . When travel time Ti is fixed and Ci changes 'Ci , the utility variation 'V1 with low income variable I q is greater than the utility variation 'V2 with high income variable I q . This means that travelers with low income are more sensitive to travel costs. Consequently, we can assume that the relation between I q and ȕi is as follows:
ȕi
Ȧi
Ȝi Iq
(5)
ȕi
Ȧi
Ȝi LnI q
(6)
ȕi
Ȧi
Ȝi I qș
(7)
Equation (8), (9) and (10) can be deduced as three different kinds of utility function when we substitute the three assumed ȕi expressed with equation (5), (6) and (7) in equation (1). Furthermore, according to equation (3) on the utility function,
we can get three kinds of utility functions with the added income variable.
Ȧi
When ȕi
Ȝi , Iq
the utility function can be expressed as
Ln
Pi Pj
Ȧi
When ȕi
Ȝi 'Cij Iq
(8)
Ȝi 'Cij Ln I q
(9)
Ȝi 'Cij I qș
(10)
Į Ȧi 'Cij Ȗ'Tij Ȝi , Ln I q
the utility function can be expressed as
Ln
Pi Pj
When ȕi
Į Ȧi 'Cij Ȗ'Tij Ȧi
Ȝi , I qș
the utility function can be expressed as
Ln
Pi Pj
Į Ȧi 'Cij Ȗ'Tij
(3) Model optimization By analyzing the data from the SP survey using regression analysis, three VOT models, in which the income variable has the form of a polynomial, logarithmic or exponential expression, are improved and the optimal model is identified. The detailed steps are as follows: ķ The VOT model with a polynomial income variable is tested. After importing the preliminary processed data to SPSS software, we define variable names and use REGRESSION module in SPSS to output the regression equation and standard deviation of coefficients. ĸ We conduct the test of goodness of fit for the regression equation, the test of significance for regression parameters and the test of significance for the regression equation. Ĺ We repeat step ķ and ĸ and output the results when the VOT model has a logarithmic and exponential income variable. ĺ Different regression equations with three different income variable forms and test results are compared, as shown in Table 7. Ļ We compare these test results. The optimal model which has a logarithmic income variable is identified because it has the highest R and R 2 , the results of the test of significance for regression parameters are all lower than 0.05, and it has the best results of the test of significance for regression equation. Finally, the optimal VOT model is formulated as follows:
Ln Pi / Pj Į Ȧ'Cij Ȗ1'T 1ij Ȗ2 'T 2ij
Ȗ3'T 3ij Ȝ'Cij / Ln I q Ȗ1,2,3 VOT1,2,3 Ȧ Ȝ/LnI q
(11) (12)
where, Pi and Pj are the probabilities that traveler q will
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
choose the travel mode i or j and Pi Pj 1 ; VOT1 is transferring time values, VOT2 is waiting time values, and VOT3 is in-vehicle time values; 'Cij is the difference between the travel costs for the travel mode i and j, for which the unit of Yuan is used; 'T 1ij , 'T 2ij and 'T 3ij are the differences between two
transferring times, two waiting times and two in-vehicle times for the travel mode i and j, for which the unit of hour is used; I q is the income variable, for which the unit of Yuan/month is used; Į , Ȧ , Ȗ1 , Ȗ2 , Ȗ3 and Ȝ are parameters that needed to be calibrated.
Table 7 Summary of Test Results
Test of goodness of fit for regression equations
Polynomial
Logarithmic
Exponential
R2
0.845
0.851
0.850
R2
0.837
0.843
0.842
R
0.919
0.922
0.922
Value of Sig.
Value of Sig.
Value of Sig.
Constant
0.062
0.057
0.058
'C
0.000
0.000
0.213
'T1
0.014
0.013
0.013
'T2
0.000
0.000
0.000
'C / I q
0.000
——
——
'C / LnI q
——
0.000
——
'C / I qT
——
——
0.000
Test of significance for regression parameters
Test of significance for regression equations
Iq in models
Form of
Test items
T
——
——
0.000
Value of F
98.292
102.695
102.377
Value of p
0.000
0.000
0.000
3.2 Model parameters calibration The regression for data from the SP survey is performed with the SPSS software after the optimal VOT model is identified. The parameters necessary for the estimation of the
travel time values under the trip purposes of work/business and leisure, as well as with vs. without transferring are calibrated. The results are shown in Table 8.
Table 8 Model Parameters Calibration Parameters Trip purpose
Work/Business
Leisure
Į
Ȧ
Ȗ1
Ȗ2
Ȗ3
Ȝ
Without transferring
–1.48
0.035
—
–4.24
–3.78
–7.75
With transferring
–0.346
0.165
–2.46
–6.56
–4.18
–10.22
Without transferring
–1.61
-0.085
—
–3.44
–2.80
–6.93
With transferring
–0.48
0.071
–3.4
–6.06
–3.36
–8.88
3.3 Model results analysis After the parameters used to estimate the travel time values under the trip purposes of work/business and leisure are calibrated, the values of time for different trip purposes, with vs. without transferring, and different income levels are estimated according to equation (12). (1) Travel time values without transferring for work and business purpose When there is no transferring, the waiting time values and in-vehicle time values increase with the increase in income for work and business purposes (as illustrated in Fig. 1). The waiting time values are generally higher than in-vehicle time values. This demonstrates that travelers pay more attention to waiting time, and anxiety appears when travelers wait for the buses or subways.
(2) Travel time values with transferring for work and business purposes When travelers use transfer services (including transferring from bus with one-transfer trip, transferring from subway with one-transfer trip, transferring from bus with two-transfer trip or transferring from subway with two-transfer trip), the transferring time values, the waiting time values and the in-vehicle time values increase (as illustrated in Fig. 2) when the income of travelers whose trip purpose is work and business rises. Time spent waiting for bus or subway is more highly valued than in-vehicle time and transferring time, while the mean time, the transferring time values are lower than in-vehicle time values. (3) Travel time values without transferring for leisure purposes The waiting time values and in-vehicle time values (as
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
illustrated in Fig. 3) without transferring increase when income in the case of leisure purposes increases. The waiting :DLWLQJ7LPH9DOXHV
time values are higher than in-vehicle time values.
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Fig. 2 Travel Time Values with Transferring for Work and Business Purposes 7UDQVIHUULQJ7LPH9DOXHV
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Fig. 1 Travel Time Values without Transferring for Work and Business Purposes
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Fig. 3 Travel Time Values without Transferring for Leisure Purposes
(4) Travel time values with transferring for leisure purposes As travelers’ incomes rise, the value people place on transferring time, waiting time and in-vehicle time increases (as illustrated in Fig. 4) with travel (including transferring from bus with one-transfer trip, transferring from subway with one-transfer trip, transferring from bus with two-transfer trip and transferring from subway with two-transfer trip) for leisure purposes. The waiting time tends to be relatively higher than the time spent in-vehicle and transferring, while the transferring time values are almost the same as in-vehicle time values. In general, the travel time values for work and business purposes are higher than those for leisure purposes. This is because travelers must arrive at the destination on time when they have work and business trips. They feel increased time stress and are more sensitive to time than to cost. Therefore, time values for work and business purposes tend to be greater than time values for leisure purposes. This reflects the increased time stress for work and business purposes. The waiting time values are greater with transferring than those without transferring, no matter if they are for business purposes or for leisure purposes. This indicates that travelers feel more anxious when waiting for the bus or subway after transferring. The in-vehicle time values with transferring are
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Fig. 4 Travel Time Values with Transferring for Leisure Purposes
nearly equal to the time values without transferring. This is due to the fact that transferring has little impact on in-vehicle time values. The waiting time values are higher than transferring time values and in-vehicle time values for any purpose. This means that travelers have the highest anxiety level when waiting for the bus or subway.
4
Conclusions
SP survey is used to obtain travel behavior data from Beijing residents, and an improved time value model for the public transport systems was proposed in this paper. Moreover, the transferring time values, the waiting time values and the in-vehicle time values for various conditions in Beijing were obtained, which provide a support for the analysis of travel costs for the public transport system. The results indicate that time values for work purposes are generally higher than those for leisure purposes, and time values increase with the increase of travelers’ incomes. Meantime, waiting time values are higher than in-vehicle time values and transferring time values because travelers are more anxious when waiting than when in-vehicle or transferring. Transferring time is valued less than in-vehicle time for work and business purposes with transferring. This is because trips for work and business
CHEN Xumei et al. / J Transpn Sys Eng & IT, 2011, 11(4), 77í84
purposes occur during peak hours with heavy traffic flow and crowded buses or subways. Travelers are more anxious when they are in-vehicle than when they are transferring from one vehicle to another because they feel uncomfortable because of crowded circumstances and traffic congestion. Transferring time values are nearly the same as in-vehicle time values for leisure purposes (such as shopping or entertainment) with transferring. Compared with the route for work and business purposes, the route and the transferring time for of leisure purposes are more flexible. At the same time, leisure trips typically occur during off-peak hours, and the vehicle is comfortable because it is less crowded. Furthermore, in-vehicle time values for work and business purposes are higher than those for leisure purposes, with or without transfer. Comfort in vehicle is one of the reasons for this, not to mention less time stress for leisure trips. The bus or subway is less crowed during off-peak hours because work and business trips occur at peak hours, while leisure trips take place during off-peak hours. The research on travel time values involves many areas, such as traffic engineering, economics and statistics. There are a great many factors affecting travel time values. Further studies can be carried out to analyze additional factors that may influence travel time values in the future.
Acknowledgements This work was supported by the National High Technology Research and Development Program of China(863 Program).
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