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Bootstrap confidence intervals of OD and link flow
Available online at www.sciencedirect.com Available online at www.sciencedirect.com
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Transportation Research Procedia 00 (2017) 000–000 Transportation Research Procedia 00 (2017) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Transportation Research Procedia 25C (2017) 2623–2628 www.elsevier.com/locate/procedia
World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016 World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016
a a
Bootstrap confidence intervals of OD and link flow Bootstrap confidence intervals of OD and link flow Hideaki Kawaokaaa, Takuya Maruyamabb * Hideaki Kawaoka , Takuya Maruyama * Department of Civil and Environmental Engineering, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
for Environmental Policy Studies, Engineering, Kumamoto University, Kurokami, Kumamoto 860-8555, Japan Department bofCenter Civil and Kumamoto2-39-1 University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan b Center for Policy Studies, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
Abstract Abstract
This study demonstrates a bootstrap interval estimation of both OD flow and link traffic flows and its application. Although causes of OD flow fluctuation various, we focusOD the flow sampling errortraffic due byflows traveland survey. We made This studythe demonstrates a bootstrap intervalare estimation of both and link its application. aAlthough trial casethestudy using Kumamoto Metropolitan Area person tripthe survey. We error demonstrate an example interval causes of OD flow fluctuation are various, we focus sampling due by travel survey.ofWe made estimation OD and link flow and discuss its implications. a trial caseofstudy using Kumamoto Metropolitan Area person trip survey. We demonstrate an example of interval estimation OD and link flow discuss © 2017 Theof Authors. Published by and Elsevier B.V.its implications. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY.
Keywords: bootstrap , interval estimation , traffic assignment, origin-destination matrix
Keywords: bootstrap , interval estimation , traffic assignment, origin-destination matrix
1. Introduction 1. Introduction Household travel-surveys have aimed at understand the transportation situation in the target area and develop travel forecasting to evaluate transport policies. We conduct these surveys at 5-10 intervals.travel OD Household models travel-surveys have aimed at understand the usually transportation situation in the target areayear and develop matrix is one of the important outputs of travel surveys and we have generally only point estimates of OD matrix. forecasting models to evaluate transport policies. We usually conduct these surveys at 5-10 year intervals. OD This is is because travel outputs survey collects datawe of only weekday. methods do not provide matrix one ofthe theusual important of traveltravelers’ surveys and have one generally onlyCurrent point estimates of OD matrix. interval estimation of OD flow that will be useful for advanced policy analysis. This is because the usual travel survey collects travelers’ data of only one weekday. Current methods do not provide Based on these backgrounds, this will study bootstrap confidence interval estimation of OD flow that bedemonstrates useful for advanced policy analysis.intervals of OD and link flow and its applications. Sources of OD flow variation are diverse, but we focus on sampling of and travel Other intervalserror of OD linksurvey. flow and its Based on these backgrounds, this study demonstrates bootstrap confidence sources such as daily variation, seasonable variation, and non-response error are also important but not the scope of applications. Sources of OD flow variation are diverse, but we focus on sampling error of travel survey. Other this paper. Probing the sampling error will provide effective information in considering the appropriate sample rate sources such as daily variation, seasonable variation, and non-response error are also important but not the scope of in travel If the we sampling reduce the sampling rate, the accuracy of the OD matrix will the decrease. However, policy this paper.survey. Probing error will provide effective information in considering appropriate sample rate indicators required for policy evaluation is not the OD matrix but the link flows and cost-benefit ratio. Then, even if in travel survey. If we reduce the sampling rate, the accuracy of the OD matrix will decrease. However, policy indicators required for policy evaluation is not the OD matrix but the link flows and cost-benefit ratio. Then, even if
* Corresponding author. Tel: 096-342-3283, Fax: 096-342-2042. E-mail address:author. [email protected] * Corresponding Tel: 096-342-3283, Fax: 096-342-2042.
E-mail address: [email protected] 2214-241X © 2017 The Authors. Published by Elsevier B.V. Peer-review WORLDbyCONFERENCE 2214-241X ©under 2017responsibility The Authors.of Published Elsevier B.V. ON TRANSPORT RESEARCH SOCIETY. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY.
2352-1465 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY. 10.1016/j.trpro.2017.05.312
Takuya Maruyama et al. / Transportation Research Procedia 25C (2017) 2623–2628 Kawaoka & Maruyama/ Transportation Research Procedia 00 (2017) 000–000
2624 2
we do not have very precise OD matrix, precisions of links flow or cost-benefit ratio may not quite low. These considerations will have practical value in transportation planning. We use the 2012 person trip (PT) survey data in Kumamoto metropolitan area, Japan. Kumamoto PT survey adopted mail-out/mail-back self-reporting survey with web-response option and household-based response rate is 38.9%, response rate of valid sample is 35.1%, and the sampling rate of 9.8%. The population of Kumamoto metropolitan area is about one million and it means we have approximately 0.1 million samples. The basic idea of bootstrap estimation in our case is we draw random resampling from the 0.1 million samples. We repeated this procedure n times, creating n sets of OD flow. We also assign the n OD flow on road network and have n set of link flows. These n sets of OD and link flows will approximate the distribution of these data and we have these confidence interval. It is also easy to simulate the situation if we change the sampling rate from 9.8% to 1% for example. 2.
Bootstrap Method
Bootstrap is one of statistical methods for assessing the distribution of the data and it was proposed by Efron (1979). By using the bootstrap method, it becomes possible to estimate the error of estimates from any sample. Classical analytical formula for calculating confidence intervals is replaced by a simple simulation with huge numerical calculations. By using the bootstrap method, it is possible to evaluate the standard errors and confidence intervals even if the observed variable is not normally distributed. For that reason, various analysis has been widely applied in complex problems and relaxing the assumptions underlying the data analysis. Non-parametric bootstrap method infers based on the empirical distribution of data without assuming a probability distribution. Parametric bootstrap method assumes the probability distribution of data. We use the nonparametric bootstrap method in this study because obtaining probability distribution of OD flow is not easy. 3. Case Study This study was carried out using Kumamoto PT survey (2012). We show the procedures here. We use the master data of Kumamoto PT survey. Target area in Kumamoto metropolitan area has total population of 1.04 million. We use B zone data of gender and age population. We neglect the trip toward/inward outside the metropolitan area. Target sample is 73,266 person data with a trip to the Kumamoto within master data of Kumamoto PT survey. We resamples from then to make bootstrap. For each resampled data, we set the expansion factor based on
Overall view
Number of road link
5,796
Number of centroid 51 Fig. 1. Road network of Kumamoto metropolitan area
Takuya Maruyama et al. / Transportation Research Procedia 25C (2017) 2623–2628 Author name / Transportation Research Procedia 00 (2017) 000–000
2625 3
population distribution. Then, we convert expanded data to OD matrix. User equilibrium model assign OD flow on the road network and we have link flow. We use network data by Fuji and Maruyama (2015). Figure 1 shows an overview of the road network data. 4. Results 4.1. Study of sampling iterations We consider the appropriate sampling iterations to obtain stable results. We change the number of iterations from 100, 1,000, 2,000, 5,000, 10,000, 20,000, and 50,000. Figure 2 shows in the plot the average number of trips for each number of iterations. We see that if the number of iterations is more than 5,000 times, we have stable results. Figure 3 shows the coefficient of variation due to the change in the number of iterations. This value gets stable after 5,000 iterations, too. Therefore, we set the number of iterations 5,000 in this study. 4.2. Population and the total number of trips Kumamoto city has five ward: Center, East, West, South, and North. Table 1 shows population of each ward. Figure 4 shows the average of the number of trips to Center-ward from each ward. We have highest number of trip from East-ward to Center-ward and lowest number of trip from North-ward. 4.3. Interval estimation of OD flow and link flow Figure 5 shows the distribution of the average trips towards the Center-ward. Red line indicates the 95% confidence intervals in the figure. OD traffic flow was assigned to the links of Kumamoto metropolitan area. Because of constraints of computational time, we show the results by 100 time iterations. The average and coefficient of variation of link flows are shown in Figure 6 and 7. Figure 8 illustrates an example of link flow distribution.
5. Summary This study shows the interval estimation of OD and link traffic flows by the bootstrap method and its trial applications. In our case study 5,000 iteration is needed to have stable output of bootstrap confidence interval estimation. This study is still in on going and we will show additional output at the conference. Specially, we will make the interval estimation of the cost-benefit ratio and policy evaluation measures.
42626
Kawaoka & Maruyama/ Research Procedia 00 (2017) Takuya Maruyama Transportation et al. / Transportation Research Procedia 25C000–000 (2017) 2623–2628
(a) East→Center
(c) South→Center
(b) West→Center
(d) Nouth→Center
Fig. 2 Number of iterations and the average number of trip
Tab.1. 2012 Population in Kumamoto wards
Center East West South North
Fig. 3 Coefficient of variation of number trip
Total population 196,521 190,482 93,620 125,458 147,595
Male
Female
89,944 90,442 43,709 59,419 70,433
106,577 100,040 49,911 66,039 77,162
Takuya Maruyama et al. / Transportation Research Procedia 25C (2017) 2623–2628 Author name / Transportation Research Procedia 00 (2017) 000–000
North Ward
West Ward
Center Ward
East Ward
South Ward unit: trip
Fig. 4 Number of Trips to the Central-ward
(a) East→Center
(c) South→Center
(b) West→Center
(d) Nouth→Center
Fig. 5 Distribution of OD flow
2627 5
Takuya Maruyama et al. / Transportation Research Procedia 25C 000–000 (2017) 2623–2628 Kawaoka & Maruyama/ Transportation Research Procedia 00 (2017)
62628
Fig. 6 Average link flow
Fig. 7 The coefficient of variation of the link flow
Fig. 8 Example of distribution of link flow (Link in front of Kumamoto City Hall )
References Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap pp.10–16，1993． Shoki Fuji, Takuya Maruyama (2015) Long-term travel forecasting using trip-chain-based user equilibrium model : proposal and validation of a quick method, Proceedings of JSTE Annual Meeting.
ScienceDirect ScienceDirect Available online at www.sciencedirect.com
Transportation Research Procedia 00 (2017) 000–000 Transportation Research Procedia 00 (2017) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Transportation Research Procedia 25C (2017) 2623–2628 www.elsevier.com/locate/procedia
World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016 World Conference on Transport Research - WCTR 2016 Shanghai. 10-15 July 2016
a a
Bootstrap confidence intervals of OD and link flow Bootstrap confidence intervals of OD and link flow Hideaki Kawaokaaa, Takuya Maruyamabb * Hideaki Kawaoka , Takuya Maruyama * Department of Civil and Environmental Engineering, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
for Environmental Policy Studies, Engineering, Kumamoto University, Kurokami, Kumamoto 860-8555, Japan Department bofCenter Civil and Kumamoto2-39-1 University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan b Center for Policy Studies, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japan
Abstract Abstract
This study demonstrates a bootstrap interval estimation of both OD flow and link traffic flows and its application. Although causes of OD flow fluctuation various, we focusOD the flow sampling errortraffic due byflows traveland survey. We made This studythe demonstrates a bootstrap intervalare estimation of both and link its application. aAlthough trial casethestudy using Kumamoto Metropolitan Area person tripthe survey. We error demonstrate an example interval causes of OD flow fluctuation are various, we focus sampling due by travel survey.ofWe made estimation OD and link flow and discuss its implications. a trial caseofstudy using Kumamoto Metropolitan Area person trip survey. We demonstrate an example of interval estimation OD and link flow discuss © 2017 Theof Authors. Published by and Elsevier B.V.its implications. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY.
Keywords: bootstrap , interval estimation , traffic assignment, origin-destination matrix
Keywords: bootstrap , interval estimation , traffic assignment, origin-destination matrix
1. Introduction 1. Introduction Household travel-surveys have aimed at understand the transportation situation in the target area and develop travel forecasting to evaluate transport policies. We conduct these surveys at 5-10 intervals.travel OD Household models travel-surveys have aimed at understand the usually transportation situation in the target areayear and develop matrix is one of the important outputs of travel surveys and we have generally only point estimates of OD matrix. forecasting models to evaluate transport policies. We usually conduct these surveys at 5-10 year intervals. OD This is is because travel outputs survey collects datawe of only weekday. methods do not provide matrix one ofthe theusual important of traveltravelers’ surveys and have one generally onlyCurrent point estimates of OD matrix. interval estimation of OD flow that will be useful for advanced policy analysis. This is because the usual travel survey collects travelers’ data of only one weekday. Current methods do not provide Based on these backgrounds, this will study bootstrap confidence interval estimation of OD flow that bedemonstrates useful for advanced policy analysis.intervals of OD and link flow and its applications. Sources of OD flow variation are diverse, but we focus on sampling of and travel Other intervalserror of OD linksurvey. flow and its Based on these backgrounds, this study demonstrates bootstrap confidence sources such as daily variation, seasonable variation, and non-response error are also important but not the scope of applications. Sources of OD flow variation are diverse, but we focus on sampling error of travel survey. Other this paper. Probing the sampling error will provide effective information in considering the appropriate sample rate sources such as daily variation, seasonable variation, and non-response error are also important but not the scope of in travel If the we sampling reduce the sampling rate, the accuracy of the OD matrix will the decrease. However, policy this paper.survey. Probing error will provide effective information in considering appropriate sample rate indicators required for policy evaluation is not the OD matrix but the link flows and cost-benefit ratio. Then, even if in travel survey. If we reduce the sampling rate, the accuracy of the OD matrix will decrease. However, policy indicators required for policy evaluation is not the OD matrix but the link flows and cost-benefit ratio. Then, even if
* Corresponding author. Tel: 096-342-3283, Fax: 096-342-2042. E-mail address:author. [email protected] * Corresponding Tel: 096-342-3283, Fax: 096-342-2042.
E-mail address: [email protected] 2214-241X © 2017 The Authors. Published by Elsevier B.V. Peer-review WORLDbyCONFERENCE 2214-241X ©under 2017responsibility The Authors.of Published Elsevier B.V. ON TRANSPORT RESEARCH SOCIETY. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY.
2352-1465 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of WORLD CONFERENCE ON TRANSPORT RESEARCH SOCIETY. 10.1016/j.trpro.2017.05.312
Takuya Maruyama et al. / Transportation Research Procedia 25C (2017) 2623–2628 Kawaoka & Maruyama/ Transportation Research Procedia 00 (2017) 000–000
2624 2
we do not have very precise OD matrix, precisions of links flow or cost-benefit ratio may not quite low. These considerations will have practical value in transportation planning. We use the 2012 person trip (PT) survey data in Kumamoto metropolitan area, Japan. Kumamoto PT survey adopted mail-out/mail-back self-reporting survey with web-response option and household-based response rate is 38.9%, response rate of valid sample is 35.1%, and the sampling rate of 9.8%. The population of Kumamoto metropolitan area is about one million and it means we have approximately 0.1 million samples. The basic idea of bootstrap estimation in our case is we draw random resampling from the 0.1 million samples. We repeated this procedure n times, creating n sets of OD flow. We also assign the n OD flow on road network and have n set of link flows. These n sets of OD and link flows will approximate the distribution of these data and we have these confidence interval. It is also easy to simulate the situation if we change the sampling rate from 9.8% to 1% for example. 2.
Bootstrap Method
Bootstrap is one of statistical methods for assessing the distribution of the data and it was proposed by Efron (1979). By using the bootstrap method, it becomes possible to estimate the error of estimates from any sample. Classical analytical formula for calculating confidence intervals is replaced by a simple simulation with huge numerical calculations. By using the bootstrap method, it is possible to evaluate the standard errors and confidence intervals even if the observed variable is not normally distributed. For that reason, various analysis has been widely applied in complex problems and relaxing the assumptions underlying the data analysis. Non-parametric bootstrap method infers based on the empirical distribution of data without assuming a probability distribution. Parametric bootstrap method assumes the probability distribution of data. We use the nonparametric bootstrap method in this study because obtaining probability distribution of OD flow is not easy. 3. Case Study This study was carried out using Kumamoto PT survey (2012). We show the procedures here. We use the master data of Kumamoto PT survey. Target area in Kumamoto metropolitan area has total population of 1.04 million. We use B zone data of gender and age population. We neglect the trip toward/inward outside the metropolitan area. Target sample is 73,266 person data with a trip to the Kumamoto within master data of Kumamoto PT survey. We resamples from then to make bootstrap. For each resampled data, we set the expansion factor based on
Overall view
Number of road link
5,796
Number of centroid 51 Fig. 1. Road network of Kumamoto metropolitan area
Takuya Maruyama et al. / Transportation Research Procedia 25C (2017) 2623–2628 Author name / Transportation Research Procedia 00 (2017) 000–000
2625 3
population distribution. Then, we convert expanded data to OD matrix. User equilibrium model assign OD flow on the road network and we have link flow. We use network data by Fuji and Maruyama (2015). Figure 1 shows an overview of the road network data. 4. Results 4.1. Study of sampling iterations We consider the appropriate sampling iterations to obtain stable results. We change the number of iterations from 100, 1,000, 2,000, 5,000, 10,000, 20,000, and 50,000. Figure 2 shows in the plot the average number of trips for each number of iterations. We see that if the number of iterations is more than 5,000 times, we have stable results. Figure 3 shows the coefficient of variation due to the change in the number of iterations. This value gets stable after 5,000 iterations, too. Therefore, we set the number of iterations 5,000 in this study. 4.2. Population and the total number of trips Kumamoto city has five ward: Center, East, West, South, and North. Table 1 shows population of each ward. Figure 4 shows the average of the number of trips to Center-ward from each ward. We have highest number of trip from East-ward to Center-ward and lowest number of trip from North-ward. 4.3. Interval estimation of OD flow and link flow Figure 5 shows the distribution of the average trips towards the Center-ward. Red line indicates the 95% confidence intervals in the figure. OD traffic flow was assigned to the links of Kumamoto metropolitan area. Because of constraints of computational time, we show the results by 100 time iterations. The average and coefficient of variation of link flows are shown in Figure 6 and 7. Figure 8 illustrates an example of link flow distribution.
5. Summary This study shows the interval estimation of OD and link traffic flows by the bootstrap method and its trial applications. In our case study 5,000 iteration is needed to have stable output of bootstrap confidence interval estimation. This study is still in on going and we will show additional output at the conference. Specially, we will make the interval estimation of the cost-benefit ratio and policy evaluation measures.
42626
Kawaoka & Maruyama/ Research Procedia 00 (2017) Takuya Maruyama Transportation et al. / Transportation Research Procedia 25C000–000 (2017) 2623–2628
(a) East→Center
(c) South→Center
(b) West→Center
(d) Nouth→Center
Fig. 2 Number of iterations and the average number of trip
Tab.1. 2012 Population in Kumamoto wards
Center East West South North
Fig. 3 Coefficient of variation of number trip
Total population 196,521 190,482 93,620 125,458 147,595
Male
Female
89,944 90,442 43,709 59,419 70,433
106,577 100,040 49,911 66,039 77,162
Takuya Maruyama et al. / Transportation Research Procedia 25C (2017) 2623–2628 Author name / Transportation Research Procedia 00 (2017) 000–000
North Ward
West Ward
Center Ward
East Ward
South Ward unit: trip
Fig. 4 Number of Trips to the Central-ward
(a) East→Center
(c) South→Center
(b) West→Center
(d) Nouth→Center
Fig. 5 Distribution of OD flow
2627 5
Takuya Maruyama et al. / Transportation Research Procedia 25C 000–000 (2017) 2623–2628 Kawaoka & Maruyama/ Transportation Research Procedia 00 (2017)
62628
Fig. 6 Average link flow
Fig. 7 The coefficient of variation of the link flow
Fig. 8 Example of distribution of link flow (Link in front of Kumamoto City Hall )
References Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap pp.10–16，1993． Shoki Fuji, Takuya Maruyama (2015) Long-term travel forecasting using trip-chain-based user equilibrium model : proposal and validation of a quick method, Proceedings of JSTE Annual Meeting.