IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v93y2016ipap225-250.html
   My bibliography  Save this article

Capacitated transit service network design with boundedly rational agents

Author

Listed:
  • Liu, Jiangtao
  • Zhou, Xuesong

Abstract

This paper proposes a new alternative modeling framework to systemically account for boundedly rational decision rules of travelers in a dynamic transit service network with tight capacity constraints. Within a time-discretized space-time network, the time-dependent transit services are characterized by traveling arcs and waiting arcs with constant travel times. Instead of using traditional flow-based formulations, an agent-based integer linear formulation is proposed to represent boundedly rational decisions under strictly imposed capacity constraints, due to vehicle carrying capacity and station storage capacity. Focusing on a viable and limited sets of space-time path alternatives, the proposed single-level optimization model can be effectively decomposed to a time-dependent routing sub-problem for individual agents and a knapsack sub-problem for service arc selections through the Lagrangian decomposition. In addition, several practically important modeling issues are discussed, such as dynamic and personalized transit pricing, passenger inflow control as part of network restraint strategies, and penalty for early/late arrival. Finally, numerical experiments are performed to demonstrate the methodology and computational efficiency of our proposed model and algorithm.

Suggested Citation

  • Liu, Jiangtao & Zhou, Xuesong, 2016. "Capacitated transit service network design with boundedly rational agents," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 225-250.
  • Handle: RePEc:eee:transb:v:93:y:2016:i:pa:p:225-250
    DOI: 10.1016/j.trb.2016.07.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516301047
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.trb.2016.07.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luathep, Paramet & Sumalee, Agachai & Lam, William H.K. & Li, Zhi-Chun & Lo, Hong K., 2011. "Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 808-827, June.
    2. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    3. Hamdouch, Younes & Szeto, W.Y. & Jiang, Y., 2014. "A new schedule-based transit assignment model with travel strategies and supply uncertainties," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 35-67.
    4. Wang, David Z.W. & Liu, Haoxiang & Szeto, W.Y., 2015. "A novel discrete network design problem formulation and its global optimization solution algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 213-230.
    5. Omar Drissi-Kaïtouni & Abdelhamid Hameda-Benchekroun, 1992. "A Dynamic Traffic Assignment Model and a Solution Algorithm," Transportation Science, INFORMS, vol. 26(2), pages 119-128, May.
    6. Wang, Shuaian & Meng, Qiang & Yang, Hai, 2013. "Global optimization methods for the discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 42-60.
    7. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    8. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    9. Mokhtarian, Patricia L. & Chen, Cynthia, 2004. "TTB or not TTB, that is the question: a review and analysis of the empirical literature on travel time (and money) budgets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(9-10), pages 643-675.
    10. Han, Ke & Szeto, W.Y. & Friesz, Terry L., 2015. "Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 16-49.
    11. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    12. Hamdouch, Younes & Lawphongpanich, Siriphong, 2008. "Schedule-based transit assignment model with travel strategies and capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 663-684, August.
    13. Drezner, Zvi & Wesolowsky, George O., 2003. "Network design: selection and design of links and facility location," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(3), pages 241-256, March.
    14. Cepeda, M. & Cominetti, R. & Florian, M., 2006. "A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 437-459, July.
    15. Guo, Xiaolei & Liu, Henry X., 2011. "Bounded rationality and irreversible network change," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1606-1618.
    16. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    17. Nie, Yu & Zhang, H. M. & Lee, Der-Horng, 2004. "Models and algorithms for the traffic assignment problem with link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 285-312, May.
    18. Patrice Marcotte & Sang Nguyen & Alexandre Schoeb, 2004. "A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks," Operations Research, INFORMS, vol. 52(2), pages 191-212, April.
    19. Szeto, W.Y. & Jiang, Y., 2014. "Transit route and frequency design: Bi-level modeling and hybrid artificial bee colony algorithm approach," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 235-263.
    20. Larry J. Leblanc, 1975. "An Algorithm for the Discrete Network Design Problem," Transportation Science, INFORMS, vol. 9(3), pages 183-199, August.
    21. Yin, Jiateng & Tang, Tao & Yang, Lixing & Gao, Ziyou & Ran, Bin, 2016. "Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 178-210.
    22. Niu, Huimin & Zhou, Xuesong & Gao, Ruhu, 2015. "Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 117-135.
    23. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    24. Poon, M. H. & Wong, S. C. & Tong, C. O., 2004. "A dynamic schedule-based model for congested transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 343-368, May.
    25. Lam, W. H. K. & Gao, Z. Y. & Chan, K. S. & Yang, H., 1999. "A stochastic user equilibrium assignment model for congested transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 33(5), pages 351-368, June.
    26. Farvaresh, Hamid & Sepehri, Mohammad Mehdi, 2011. "A single-level mixed integer linear formulation for a bi-level discrete network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 623-640, September.
    27. Lou, Yingyan & Yin, Yafeng & Lawphongpanich, Siriphong, 2010. "Robust congestion pricing under boundedly rational user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 15-28, January.
    28. Poorzahedy, Hossain & Rouhani, Omid M., 2007. "Hybrid meta-heuristic algorithms for solving network design problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 578-596, October.
    29. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    30. Joaquín de Cea & Enrique Fernández, 1993. "Transit Assignment for Congested Public Transport Systems: An Equilibrium Model," Transportation Science, INFORMS, vol. 27(2), pages 133-147, May.
    31. Agostino Nuzzolo & Francesco Russo & Umberto Crisalli, 2001. "A Doubly Dynamic Schedule-based Assignment Model for Transit Networks," Transportation Science, INFORMS, vol. 35(3), pages 268-285, August.
    32. Di, Xuan & Liu, Henry X. & Pang, Jong-Shi & Ban, Xuegang (Jeff), 2013. "Boundedly rational user equilibria (BRUE): Mathematical formulation and solution sets," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 300-313.
    33. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    34. Hani S. Mahmassani & Gang-Len Chang, 1987. "On Boundedly Rational User Equilibrium in Transportation Systems," Transportation Science, INFORMS, vol. 21(2), pages 89-99, May.
    35. Wang, David Z.W. & Lo, Hong K., 2010. "Global optimum of the linearized network design problem with equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 482-492, May.
    36. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    37. Tong, Lu & Zhou, Xuesong & Miller, Harvey J., 2015. "Transportation network design for maximizing space–time accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 555-576.
    38. Li, Pengfei & Mirchandani, Pitu & Zhou, Xuesong, 2015. "Solving simultaneous route guidance and traffic signal optimization problem using space-phase-time hypernetwork," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 103-130.
    39. Di, Xuan & Liu, Henry X. & Ban, Xuegang (Jeff), 2016. "Second best toll pricing within the framework of bounded rationality," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 74-90.
    40. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    41. Tian, Qiong & Huang, Hai-Jun & Yang, Hai, 2007. "Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 616-631, July.
    42. Gao, Ziyou & Wu, Jianjun & Sun, Huijun, 2005. "Solution algorithm for the bi-level discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(6), pages 479-495, July.
    43. Mahmoudi, Monirehalsadat & Zhou, Xuesong, 2016. "Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 19-42.
    44. Sang Nguyen & Stefano Pallottino & Federico Malucelli, 2001. "A Modeling Framework for Passenger Assignment on a Transport Network with Timetables," Transportation Science, INFORMS, vol. 35(3), pages 238-249, August.
    45. Ibarra-Rojas, O.J. & Delgado, F. & Giesen, R. & Muñoz, J.C., 2015. "Planning, operation, and control of bus transport systems: A literature review," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 38-75.
    46. Yang, Lixing & Zhang, Yan & Li, Shukai & Gao, Yuan, 2016. "A two-stage stochastic optimization model for the transfer activity choice in metro networks," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 271-297.
    47. Di, Xuan & He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2014. "Braess paradox under the boundedly rational user equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 86-108.
    48. Guihaire, Valérie & Hao, Jin-Kao, 2008. "Transit network design and scheduling: A global review," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(10), pages 1251-1273, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shang, Pan & Li, Ruimin & Guo, Jifu & Xian, Kai & Zhou, Xuesong, 2019. "Integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network: A space-time-state hyper network-based assignment approach," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 135-167.
    2. Khani, Alireza, 2019. "An online shortest path algorithm for reliable routing in schedule-based transit networks considering transfer failure probability," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 549-564.
    3. Wang, David Z.W. & Liu, Haoxiang & Szeto, W.Y., 2015. "A novel discrete network design problem formulation and its global optimization solution algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 213-230.
    4. Tian, Qingyun & Wang, David Z.W. & Lin, Yun Hui, 2021. "Service operation design in a transit network with congested common lines," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 81-102.
    5. Jiang, Y. & Szeto, W.Y., 2016. "Reliability-based stochastic transit assignment: Formulations and capacity paradox," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 181-206.
    6. Liu, Haoxiang & Szeto, W.Y. & Long, Jiancheng, 2019. "Bike network design problem with a path-size logit-based equilibrium constraint: Formulation, global optimization, and matheuristic," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 284-307.
    7. Cancela, Héctor & Mauttone, Antonio & Urquhart, María E., 2015. "Mathematical programming formulations for transit network design," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 17-37.
    8. Li, Guoyuan & Chen, Anthony, 2023. "Strategy-based transit stochastic user equilibrium model with capacity and number-of-transfers constraints," European Journal of Operational Research, Elsevier, vol. 305(1), pages 164-183.
    9. Fontaine, Pirmin & Minner, Stefan, 2014. "Benders Decomposition for Discrete–Continuous Linear Bilevel Problems with application to traffic network design," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 163-172.
    10. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    11. Codina, Esteve & Rosell, Francisca, 2017. "A heuristic method for a congested capacitated transit assignment model with strategies," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 293-320.
    12. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    13. Hamdouch, Younes & Szeto, W.Y. & Jiang, Y., 2014. "A new schedule-based transit assignment model with travel strategies and supply uncertainties," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 35-67.
    14. Elnaz Miandoabchi & Reza Farahani & W. Szeto, 2012. "Bi-objective bimodal urban road network design using hybrid metaheuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 583-621, December.
    15. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    16. Tan, Zhijia & Yang, Hai & Tan, Wei & Li, Zhichun, 2016. "Pareto-improving transportation network design and ownership regimes," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 292-309.
    17. Binder, Stefan & Maknoon, Yousef & Bierlaire, Michel, 2017. "Exogenous priority rules for the capacitated passenger assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 19-42.
    18. Di, Zhen & Yang, Lixing & Qi, Jianguo & Gao, Ziyou, 2018. "Transportation network design for maximizing flow-based accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 209-238.
    19. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    20. Kumar, Pramesh & Khani, Alireza, 2022. "Planning of integrated mobility-on-demand and urban transit networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 166(C), pages 499-521.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:93:y:2016:i:pa:p:225-250. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.