IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v323y2025i2p504-524.html
   My bibliography  Save this article

An operation-agnostic stochastic user equilibrium model for mobility-on-demand networks with congestible capacities

Author

Listed:
  • Liu, Bingqing
  • Watling, David
  • Chow, Joseph Y.J.

Abstract

Evaluating the impact of privately-owned Mobility-on-Demand (MoD) services is important from a regulatory perspective. There is a need to model multimodal equilibria with MoD to support policymaking. While there exists a large body of literature on MoD services focusing on service design under equilibrium modeling, these studies commonly adopt assumptions of MoD operational policies. However, such policies might not be shared with regulatory agencies due to commercial privacy concerns of private operators. We model multimodal equilibrium with MoD systems in an operation-agnostic manner based on empirical observations of flow and capacity. This is done with a Flow-Capacity Interaction (FC) matrix that captures systematic effect of congestible capacities, a phenomenon in MoD systems where capacities are affected by flows. The FC matrix encapsulates the operation and demand patterns by capturing the empirical equilibrium relationship between flows and capacities. An operation-agnostic logit-based stochastic user equilibrium (SUE) formulation is proposed and proof of equivalence of the SUE formulation is derived. The proof shows that, unlike static capacities, path delays are not just the sum of the Lagrange multipliers of the links on the paths, but dependent on the whole network. We name this phenomenon as “non-separable link delays”. A solution algorithm that finds SUE with a bounded path set is proposed, with a custom Frank-Wolfe algorithm to solve the non-linear SUE formulation. Since the FC matrix cannot be directly observed, an inverse optimization problem is introduced to estimate it with observed flow and capacity data. Two numerical examples are provided with sensitivity tests. An empirical example with yellow taxi data of downtown Manhattan, NY is provided to demonstrate effectiveness of estimating the FC matrix from real data, and for determining the equilibrium that captures the underlying flow-capacity dynamics.

Suggested Citation

  • Liu, Bingqing & Watling, David & Chow, Joseph Y.J., 2025. "An operation-agnostic stochastic user equilibrium model for mobility-on-demand networks with congestible capacities," European Journal of Operational Research, Elsevier, vol. 323(2), pages 504-524.
    • Handle: RePEc:eee:ejores:v:323:y:2025:i:2:p:504-524
    DOI: 10.1016/j.ejor.2024.12.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724009809
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.12.038?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Martin L. Hazelton & David P. Watling, 2004. "Computation of Equilibrium Distributions of Markov Traffic-Assignment Models," Transportation Science, INFORMS, vol. 38(3), pages 331-342, August.
    2. Ravindra K. Ahuja & James B. Orlin, 2001. "Inverse Optimization," Operations Research, INFORMS, vol. 49(5), pages 771-783, October.
    3. Li, Yuanyuan & Liu, Yang & Xie, Jun, 2020. "A path-based equilibrium model for ridesharing matching," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 373-405.
    4. Lin, Jenn-Rong & Yang, Ta-Hui, 2011. "Strategic design of public bicycle sharing systems with service level constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(2), pages 284-294, March.
    5. Pel, Adam J. & Chaniotakis, Emmanouil, 2017. "Stochastic user equilibrium traffic assignment with equilibrated parking search routes," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 123-139.
    6. Yang, Hai & Yang, Teng, 2011. "Equilibrium properties of taxi markets with search frictions," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 696-713, May.
    7. Sayarshad, Hamid R. & Chow, Joseph Y.J., 2017. "Non-myopic relocation of idle mobility-on-demand vehicles as a dynamic location-allocation-queueing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 60-77.
    8. Ke, Jintao & Yang, Hai & Li, Xinwei & Wang, Hai & Ye, Jieping, 2020. "Pricing and equilibrium in on-demand ride-pooling markets," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 411-431.
    9. Sun, S. & Szeto, W.Y., 2021. "Multi-class stochastic user equilibrium assignment model with ridesharing: Formulation and policy implications," Transportation Research Part A: Policy and Practice, Elsevier, vol. 145(C), pages 203-227.
    10. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    11. Yang, Hai & Wong, S. C. & Wong, K. I., 2002. "Demand-supply equilibrium of taxi services in a network under competition and regulation," Transportation Research Part B: Methodological, Elsevier, vol. 36(9), pages 799-819, November.
    12. Susan Jia Xu & Mehdi Nourinejad & Xuebo Lai & Joseph Y. J. Chow, 2018. "Network Learning via Multiagent Inverse Transportation Problems," Service Science, INFORMS, vol. 52(6), pages 1347-1364, December.
    13. 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.
    14. Yang, Hai & Wong, S. C., 1998. "A network model of urban taxi services," Transportation Research Part B: Methodological, Elsevier, vol. 32(4), pages 235-246, May.
    15. Sang Nguyen & Clermont Dupuis, 1984. "An Efficient Method for Computing Traffic Equilibria in Networks with Asymmetric Transportation Costs," Transportation Science, INFORMS, vol. 18(2), pages 185-202, May.
    16. Sayarshad, Hamid R. & Chow, Joseph Y.J., 2015. "A scalable non-myopic dynamic dial-a-ride and pricing problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 539-554.
    17. Zhang, Yufeng & Khani, Alireza, 2021. "Integrating transit systems with ride-sourcing services: A study on the system users’ stochastic equilibrium problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 150(C), pages 95-123.
    18. Wong, K.I. & Wong, S.C. & Yang, Hai & Wu, J.H., 2008. "Modeling urban taxi services with multiple user classes and vehicle modes," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 985-1007, December.
    19. Noruzoliaee, Mohamadhossein & Zou, Bo, 2022. "One-to-many matching and section-based formulation of autonomous ridesharing equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 72-100.
    20. Di, Xuan & Ban, Xuegang Jeff, 2019. "A unified equilibrium framework of new shared mobility systems," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 50-78.
    21. Rasmussen, Thomas Kjær & Duncan, Lawrence Christopher & Watling, David Paul & Nielsen, Otto Anker, 2024. "Local detouredness: A new phenomenon for modelling route choice and traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 190(C).
    22. Wong, K. I. & Wong, S. C. & Yang, Hai, 2001. "Modeling urban taxi services in congested road networks with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 35(9), pages 819-842, November.
    23. Frade, Ines & Ribeiro, Anabela, 2015. "Bike-sharing stations: A maximal covering location approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 82(C), pages 216-227.
    24. Xu, Huayu & Pang, Jong-Shi & Ordóñez, Fernando & Dessouky, Maged, 2015. "Complementarity models for traffic equilibrium with ridesharing," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 161-182.
    25. (Jeff) Ban, Xuegang & Dessouky, Maged & Pang, Jong-Shi & Fan, Rong, 2019. "A general equilibrium model for transportation systems with e-hailing services and flow congestion," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 273-304.
    26. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2018. "Stochastic user equilibrium with a bounded choice model," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 254-280.
    27. Park, Chung & Sohn, So Young, 2017. "An optimization approach for the placement of bicycle-sharing stations to reduce short car trips: An application to the city of Seoul," Transportation Research Part A: Policy and Practice, Elsevier, vol. 105(C), pages 154-166.
    28. Ma, Jie & Xu, Min & Meng, Qiang & Cheng, Lin, 2020. "Ridesharing user equilibrium problem under OD-based surge pricing strategy," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 1-24.
    29. Hanif D. Sherali & Antoine G. Hobeika & Sasikul Kangwalklai, 2003. "Time-Dependent, Label-Constrained Shortest Path Problems with Applications," Transportation Science, INFORMS, vol. 37(3), pages 278-293, August.
    30. 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.
    31. Di, Xuan & Liu, Henry X., 2016. "Boundedly rational route choice behavior: A review of models and methodologies," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 142-179.
    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. Haider, Zulqarnain & Nikolaev, Alexander & Kang, Jee Eun & Kwon, Changhyun, 2018. "Inventory rebalancing through pricing in public bike sharing systems," European Journal of Operational Research, Elsevier, vol. 270(1), pages 103-117.
    34. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    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. Di, Xuan & Ban, Xuegang Jeff, 2019. "A unified equilibrium framework of new shared mobility systems," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 50-78.
    2. Noruzoliaee, Mohamadhossein & Zou, Bo, 2022. "One-to-many matching and section-based formulation of autonomous ridesharing equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 72-100.
    3. Rui Yao & Shlomo Bekhor, 2023. "A general equilibrium model for multi-passenger ridesharing systems with stable matching," Papers 2303.16595, arXiv.org, revised Dec 2023.
    4. Yao, Rui & Bekhor, Shlomo, 2023. "A general equilibrium model for multi-passenger ridesharing systems with stable matching," Transportation Research Part B: Methodological, Elsevier, vol. 175(C).
    5. Li, Tongfei & Xu, Min & Sun, Huijun & Xiong, Jie & Dou, Xueping, 2023. "Stochastic ridesharing equilibrium problem with compensation optimization," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 170(C).
    6. Tan, Heqing & Xu, Xiangdong & Chen, Anthony, 2024. "On endogenously distinguishing inactive paths in stochastic user equilibrium: A convex programming approach with a truncated path choice model," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    7. Li, Tongfei & Ge, Yao & Xiong, Jie & Xu, Min & Wu, Jianjun & Sun, Huijun, 2024. "Ridesharing user equilibrium model without the en-route transfer: An OD-based link-node formulation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 187(C).
    8. Valentina Morandi, 2024. "Bridging the user equilibrium and the system optimum in static traffic assignment: a review," 4OR, Springer, vol. 22(1), pages 89-119, March.
    9. Ting Wang & Yong Zhang & Meiye Li & Lei Liu, 2019. "How Do Passengers with Different Using Frequencies Choose between Traditional Taxi Service and Online Car-Hailing Service? A Case Study of Nanjing, China," Sustainability, MDPI, vol. 11(23), pages 1-18, November.
    10. Sun, Mingmei, 2023. "A day-to-day dynamic model for mixed traffic flow of autonomous vehicles and inertial human-driven vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    11. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.
    12. Li, Baicheng & Szeto, W.Y., 2021. "Modeling and analyzing a taxi market with a monopsony taxi owner and multiple rentee-drivers," Transportation Research Part B: Methodological, Elsevier, vol. 143(C), pages 1-22.
    13. Li, Sen & Yang, Hai & Poolla, Kameshwar & Varaiya, Pravin, 2021. "Spatial pricing in ride-sourcing markets under a congestion charge," Transportation Research Part B: Methodological, Elsevier, vol. 152(C), pages 18-45.
    14. (Jeff) Ban, Xuegang & Dessouky, Maged & Pang, Jong-Shi & Fan, Rong, 2019. "A general equilibrium model for transportation systems with e-hailing services and flow congestion," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 273-304.
    15. Thorsten Heilker & Gernot Sieg, 2017. "A duopoly of transportation network companies and traditional radio-taxi dispatch service agencies," Working Papers 24, Institute of Transport Economics, University of Muenster.
    16. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2018. "Stochastic user equilibrium with a bounded choice model," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 254-280.
    17. Li, Baicheng & Szeto, W.Y., 2019. "Taxi service area design: Formulation and analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 125(C), pages 308-333.
    18. Yang, Jie & Zhao, Daozhi & Wang, Zeyu & Xu, Chunqiu, 2022. "Impact of regulation on on-demand ride-sharing service: Profit-based target vs demand-based target," Research in Transportation Economics, Elsevier, vol. 92(C).
    19. Du, Muqing & Zhou, Jiankun & Chen, Anthony & Tan, Heqing, 2022. "Modeling the capacity of multimodal and intermodal urban transportation networks that incorporate emerging travel modes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    20. Wong, R.C.P. & Szeto, W.Y. & Wong, S.C., 2014. "Bi-level decisions of vacant taxi drivers traveling towards taxi stands in customer-search: Modeling methodology and policy implications," Transport Policy, Elsevier, vol. 33(C), pages 73-81.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:ejores:v:323:y:2025:i:2:p:504-524. 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/locate/eor .

    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.