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A path-based equilibrium model for ridesharing matching

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  • Li, Yuanyuan
  • Liu, Yang
  • Xie, Jun

Abstract

This paper examines how the ridesharing program will reshape the spatial distribution of traffic congestion. With ridesharing services, travelers make multi-dimensional decisions concerning mode choices, route choices, and matching decisions. We build a path-based equilibrium model to describe the decision-making of travelers in the presence of the ridesharing program and thereby to forecast the stable congestion distribution in the long run. Specifically, our model can explicitly track the path information of the matched drivers and riders by solving the proposed equilibrium model. The model is formulated as variational inequalities due to the non-separable cost functions and asymmetric link interactions. We first demonstrate the non-uniqueness of mode-specific link flows and derive the condition for the uniqueness of link flows. We then derive sufficient conditions for a matching failure. A matching failure occurs if the lowest total inconvenience cost of a pair of rider and driver exceeds a threshold. In this situation, matching between the ridesharing supply (drivers) and demand (riders) cannot be established by adjusting the compensation scheme. Moreover, we derive the sufficient and necessary conditions for the existence of equilibrium with a positive ridesharing ridership. These conditions help operators gain insights into how to appropriately design compensation schemes. We reformulate the variational inequalities as the equivalent mixed complementarity problem, and propose a heuristic routing algorithm to identify the feasible routing paths for shared rides that interest both ridesharing drivers and riders. Finally, Our numerical experiments show that ridesharing is effective in relieving the overall congestion but leads to high congestion on some links. In the scenarios where the demand into the central business district (CBD) is high, the commuters entering CBD are all better off with ridesharing service. In contrast, the commuters traveling to certain non-CBD areas are worse off. Our experiments also reveal various path choice behaviors of ridesharing participants. The solo drivers always use the paths with short travel times, while the ridesharing drivers tend to use paths with short travel distances. By considering a commission to the platform, we demonstrate the regime in which increasing the commission rate improves the platform’s revenue without harming the social welfare.

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  • 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.
    • Handle: RePEc:eee:transb:v:138:y:2020:i:c:p:373-405
    DOI: 10.1016/j.trb.2020.05.007
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    7. Fu, Hao & Lam, William H.K. & Shao, Hu & Ma, Wei & Chen, Bi Yu & Ho, H.W., 2022. "Optimization of multi-type sensor locations for simultaneous estimation of origin-destination demands and link travel times with covariance effects," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 19-47.
    8. Yi Cao & Shan Wang & Jinyang Li, 2021. "The Optimization Model of Ride-Sharing Route for Ride Hailing Considering Both System Optimization and User Fairness," Sustainability, MDPI, vol. 13(2), pages 1-17, January.
    9. Wang, Jianbiao & Miwa, Tomio & Morikawa, Takayuki, 2023. "Recursive decomposition probability model for demand estimation of street-hailing taxis utilizing GPS trajectory data," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 171-195.
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    11. 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.
    12. 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.
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    15. 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).
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    17. Tang, Zhe-Yi & Tian, Li-Jun & Wang, David Z.W., 2021. "Multi-modal morning commute with endogenous shared autonomous vehicle penetration considering parking space constraint," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 151(C).

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