Optimizing fares and transfer discounts for a bus-subway corridor
Abstract
This paper aims to optimize fares and transfer discounts for public transit service along a bus-subway corridor with the consideration of effects of uncertainty in travel times and difference in stop spacing between bus and subway services on passenger behavior. The former factor is captured by the reserved time in travel cost and the latter one produces some passenger Origin–Destination (O–D) pairs along the corridor that can not be served by one mode only. This problem is formulated as a bi-level program, of which the upper level maximizes the social welfare and the lower-level capturing traveler choice behavior is a variable-demand Stochastic User Equilibrium (SUE) assignment model. A Genetic Algorithm (GA) is applied to solve the bi-level program while the Method of Successive Averages (MSA) is adopted to solve the lower-level model. A series of numerical experiments are carried out to illustrate the performance of the model and solution method. Numerical results indicate that the implementation of transfer discounts may be of great benefit to the social welfare and that the uncertainty in travel time and the difference in stop spacing play an important role in determining optimal fares and transfer discounts for the service along a bus-subway corridor.
Keyword : transfer discount, uncertainty in travel times, stop distance, bi-level program, public transit corridor
How to Cite
Liu, B.-Z., Ge, Y.-E., Cao, K., Jiang, X., & Meng, L. (2019). Optimizing fares and transfer discounts for a bus-subway corridor. Transport, 34(6), 672-683. https://doi.org/10.3846/transport.2019.11566
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Watling, D. 2006. User equilibrium traffic network assignment with stochastic travel times and late arrival penalty, European Journal of Operational Research 175(3): 1539–1556. https://doi.org/10.1016/j.ejor.2005.02.039
Williams, H. C. W. L. 1977. On the formation of travel demand models and economic evaluation measures of user benefit, Environment and Planning A: Economy and Space 9(3): 285–344. https://doi.org/10.1068/a090285
Yang, H.; Kin, W. K. 2000. Modeling bus service under competition and regulation, Journal of Transportation Engineering 126(5): 419–425. https://doi.org/10.1061/(ASCE)0733-947X(2000)126:5(419)
Yao, B.; Hu, P.; Lu, X.; Gao, J.; Zhang, M. 2014. Transit network design based on travel time reliability, Transportation Research Part C: Emerging Technologies 43: 233–248. https://doi.org/10.1016/j.trc.2013.12.005
Yao, J.; Shi, F.; An, S.; Wang, J. 2015. Evaluation of exclusive bus lanes in a bi-modal degradable road network, Transportation Research Part C: Emerging Technologies 60: 36–51. https://doi.org/10.1016/j.trc.2015.08.005
Zhou, J.; Lam, W. H. K.; Heydecker, B. G. 2005. The generalized Nash equilibrium model for oligopolistic transit market with elastic demand, Transportation Research Part B: Methodological 39(6): 519–544. https://doi.org/10.1016/j.trb.2004.07.003
Ben-Akiva, M.; Lerman, S. R. 1985. Discrete Choice Analysis: Theory and Application to Travel Demand. MIT Press. 412 p.
Borndörfer, R.; Karbstein, M.; Pfetsch, M. E. 2012. Models for fare planning in public transport, Discrete Applied Mathematics 160(18): 2591–2605. https://doi.org/10.1016/j.dam.2012.02.027
Chen, B. Y.; Shi, C.; Zhang, J.; Lam, W. H. K.; Li, Q.; Xiang, S. 2017. Most reliable path-finding algorithm for maximizing on-time arrival probability, Transportmetrica B: Transport Dynamics 5(3): 248–264. https://doi.org/10.1080/21680566.2016.1169953
De Palma, A.; Kilani, M.; Proost, S. 2015. Discomfort in mass transit and its implication for scheduling and pricing, Transportation Research Part B: Methodological 71: 1–18. https://doi.org/10.1016/j.trb.2014.10.001
Ehrgott, M.; Wang, J. Y. T.; Watling, D. P. 2015. On multi-objective stochastic user equilibrium, Transportation Research Part B: Methodological 81: 704–717. https://doi.org/10.1016/j.trb.2015.06.013
Evans, A. 1987. A theoretical comparison of competition with other economic regimes for bus services, Journal of Transport Economics and Policy 21(1): 7–36.
Frejinger, E.; Bierlaire, M. 2007. Capturing correlation with sub-networks in route choice models, Transportation Research Part B: Methodological 41(3): 363–378. https://doi.org/10.1016/j.trb.2006.06.003
Fujii, S.; Kitamura, R. 2004. Drivers’ mental representation of travel time and departure time choice in uncertain traffic network conditions, Networks and Spatial Economics 4(3): 243–256. https://doi.org/10.1023/B:NETS.0000039781.10517.3a
Glaister, S.; Collings, J. J. 1978. Maximisation of passenger miles in theory and practice, Journal of Transport Economics and Policy 12(3): 304–321.
Kaddoura, I.; Kickhöfer, B.; Neumann, A.; Tirachini, A. 2015. Agent-based optimisation of public transport supply and pricing: impacts of activity scheduling decisions and simulation randomness, Transportation 42(6): 1039–1061. https://doi.org/10.1007/s11116-014-9533-6
Kocur, G.; Hendrickson, C. 1982. Design of local bus service with demand equilibration, Transportation Science 16(2): 149–170. https://doi.org/10.1287/trsc.16.2.149
Lam, W.; Morrall, J. 1982. Bus passenger walking distances and waiting times: a summer–winter comparison, Transportation Quarterly 36(3): 407–421.
Lam, W. H. K.; Zhou, J. 2000. Optimal fare structure for transit networks with elastic demand, Transportation Research Record: Journal of the Transportation Research Board 1733: 8–14. https://doi.org/10.3141/1733-02
Li, Z.-C.; Lam, W. H. K.; Wong, S. C. 2009a. Optimization of a bus and rail transit system with feeder bus services under different market regimes, in W. H. K. Lam, S. C. Wong, H. K. Lo (Eds.). Transportation and Traffic Theory 2009: Golden Jubilee: 495–516. https://doi.org/10.1007/978-1-4419-0820-9_25
Li, Z.-C.; Lam, W. H. K.; Wong, S. C. 2009b. The optimal transit fare structure under different market regimes with uncertainty in the network, Networks and Spatial Economics 9(2): 191–216. https://doi.org/10.1007/s11067-007-9058-z
Liu, B.-Z.; Ge, Y.-E.; Cao, K.; Jiang, X.; Meng, L.; Liu, D.; Gao, Y. 2017. Optimizing a desirable fare structure for a bus-subway corridor, Plos One 12(10): e0184815. https://doi.org/10.1371/journal.pone.0184815
Lu, X.-S.; Liu, T.-L.; Huang, H.-J. 2015. Pricing and mode choice based on nested logit model with trip-chain costs, Transport Policy 44: 76–88. https://doi.org/10.1016/j.tranpol.2015.06.014
Nash, C. A. 1978. Management objectives, fares and service levels in bus transport, Journal of Transport Economics and Policy 12(1): 70–85.
Noland, R. B.; Polak, J. W. 2002. Travel time variability: a review of theoretical and empirical issues, Transport Reviews 22(1): 39–54. https://doi.org/10.1080/01441640010022456
Oppenheim, N. 1995. Urban Travel Demand Modeling: from Individual Choices to General Equilibrium. Wiley, New York. 480 p.
Ramming, M. C. 2002. Network Knowledge and Route Choice. PhD Dissertation. Massachusetts Institute of Technology, US. 394 p. Available from Internet: https://dspace.mit.edu/handle/1721.1/49797
Shao, H.; Lam, W. H. K.; Meng, Q.; Tam, M. L. 2006. Demand-driven traffic assignment problem based on travel time reliability, Transportation Research Record: Journal of the Transportation Research Board 1985: 220–230. https://doi.org/10.1177/0361198106198500124
Sheffi, Y. 1985. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice Hall. 399 p.
Spiess, H.; Florian, M. 1989. Optimal strategies: a new assignment model for transit networks, Transportation Research Part B: Methodological 23(2): 83–102. https://doi.org/10.1016/0191-2615(89)90034-9
Tang, C.; Ceder, A.; Ge, Y.-E. 2017. Integrated optimization of bus line fare and operational strategies using elastic demand, Journal of Advanced Transportation 2017: 7058789. https://doi.org/10.1155/2017/7058789
Tang, C.; Ceder, A.; Zhao, S.; Ge, Y.-E. 2016. Determining optimal strategies for single-line bus operation by means of smartphone demand data, Transportation Research Record: Journal of the Transportation Research Board 2539: 130–139. https://doi.org/10.3141/2539-15
Tang, C.; Ge, Y.-E.; Lam, W. H. K. 2019. Optimizing limited-stop bus services along a public transit corridor with a differential fare structure, Transport 34(4): 476–489. https://doi.org/10.3846/transport.2019.11235
Tirachini, A.; Hensher, D. A. 2011. Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors, Transportation Research Part B: Methodological 45(5): 828–844. https://doi.org/10.1016/j.trb.2011.02.006
Tirachini, A.; Hensher, D. A.; Rose, J. M. 2014. Multimodal pricing and optimal design of urban public transport: the interplay between traffic congestion and bus crowding, Transportation Research Part B: Methodological 61: 33–54. https://doi.org/10.1016/j.trb.2014.01.003
Tong, C. O.; Wong, S. C. 1999. A stochastic transit assignment model using a dynamic schedule-based network, Transportation Research Part B: Methodological 33(2): 107–121. https://doi.org/10.1016/S0191-2615(98)00030-7
Wang, W.; Sun, H.; Wang, Z.; Wu, J. 2014. Optimal transit fare in a bimodal network under demand uncertainty and bounded rationality, Journal of Advanced Transportation 48(8): 957–973. https://doi.org/10.1002/atr.1238
Watling, D. 2006. User equilibrium traffic network assignment with stochastic travel times and late arrival penalty, European Journal of Operational Research 175(3): 1539–1556. https://doi.org/10.1016/j.ejor.2005.02.039
Williams, H. C. W. L. 1977. On the formation of travel demand models and economic evaluation measures of user benefit, Environment and Planning A: Economy and Space 9(3): 285–344. https://doi.org/10.1068/a090285
Yang, H.; Kin, W. K. 2000. Modeling bus service under competition and regulation, Journal of Transportation Engineering 126(5): 419–425. https://doi.org/10.1061/(ASCE)0733-947X(2000)126:5(419)
Yao, B.; Hu, P.; Lu, X.; Gao, J.; Zhang, M. 2014. Transit network design based on travel time reliability, Transportation Research Part C: Emerging Technologies 43: 233–248. https://doi.org/10.1016/j.trc.2013.12.005
Yao, J.; Shi, F.; An, S.; Wang, J. 2015. Evaluation of exclusive bus lanes in a bi-modal degradable road network, Transportation Research Part C: Emerging Technologies 60: 36–51. https://doi.org/10.1016/j.trc.2015.08.005
Zhou, J.; Lam, W. H. K.; Heydecker, B. G. 2005. The generalized Nash equilibrium model for oligopolistic transit market with elastic demand, Transportation Research Part B: Methodological 39(6): 519–544. https://doi.org/10.1016/j.trb.2004.07.003