Integrating transit systems with ride-sourcing services: A study on the system users’ stochastic equilibrium problem

Yufeng Zhang, Alireza Khani

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Ride-sourcing services are continuously gaining popularity among urban travelers. Due to their flexibility and responsiveness, transit agencies spot chances of collaborating with Transportation Network Companies (TNCs) in order to improve service quality, promote transit usage, and meanwhile lower their operational cost. In this paper, we studied an integrated transit system where ride-sourcing services complement the transit service as an efficient and economical access mode. The users of the integrated system consist of not only transit riders but also drivers for TNCs. Riders maximize their utilities by choosing whether and how to use the integrated system, and drivers maximize their payoffs by deciding how to serve riders. More importantly, in this two-sided system, their decisions are unfolded to each other and mutually influence one another such that an equilibrium is reached where no one can improve their outcome. We modeled the stochastic mode choice of riders and zone choice of drivers and captured the interactive attributes in a fixed-point problem. The existence of such an equilibrium was proved, and an iterative solution algorithm that utilizes network algorithms was proposed to find an equilibrium pattern of the stochastic demand-supply problem. A real-world case study using the Twin Cities’ data was carried out, and insights into the mechanism of the integrated transit system were developed. Various aspects of the system including user perception, demand estimation, pricing strategy, and subsidy strategy were investigated through the proposed model. These research outcomes contribute to a better comprehension of this promising mobility system and provide valuable knowledge on the planning and design of such systems.

Original languageEnglish (US)
Pages (from-to)95-123
Number of pages29
JournalTransportation Research Part A: Policy and Practice
StatePublished - Aug 2021

Bibliographical note

Funding Information:
This research is conducted at the University of Minnesota Transit Lab, currently supported by the following, but not limited to, projects: National Science Foundation, award CMMI-1831140, Freight Mobility Research Institute (FMRI), Tier 1 Transportation Center, U.S. Department of Transportation: award RR-K78/FAU SP#16-532 AM2 and AM3, Minnesota Department of Transportation, Contract No. 1003325 Work Order No. 44 and 111, Minnesota Department of Transportation, Agreement No. 1044277.

Publisher Copyright:
© 2021 Elsevier Ltd


  • Demand and supply
  • Integrated transit system
  • Mode choice
  • Public private partnership
  • Ride-sourcing
  • Stochastic equilibrium


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