One-to-many matching and section-based formulation of autonomous ridesharing equilibrium

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This paper models autonomous ridesharing — multiple travelers simultaneously riding one shared autonomous vehicle (SAV) — in a network equilibrium setting with mixed SAV and human-driven vehicle (HV) traffic. We make two major methodological contributions. First, a novel one (SAV)-to-many (riders) matching is proposed to characterize the waiting times of an SAV and multiple travelers who share rides in the SAV during online matching, which is a nontrivial generalization of the one-to-one matching without ridesharing. Our matching characterization considers the possibilities of a traveler matched with an SAV starting from the same origin, whereto the SAV moved unoccupied as a result of either pickup or relocation, or with an in-service SAV that goes through the traveler's origin. Second, a section-based formulation for SAV ridesharing user equilibrium is introduced to characterize the SAV traveler flow, which accommodates the possibility that an SAV traveler's itinerary (OD pair) is different from that of the serving SAV and other travelers in the SAV. Unlike the existing link and route based ridesharing formulations, the notion of section both prevents undesired traveler en-route transfer(s) and allows travelers of multiple ODs to share rides, meanwhile respecting the SAV seat capacity constraint. In addition to the above two methodological contributions, the optimal SAV fleet size, fare, routing, and allocation (to in-service, pickup, and relocation states) decisions of a transportation network company (TNC) are formulated. The TNC decisions anticipate traveler reactions as characterized by a new multimodal autonomous ridesharing user equilibrium (MARUE), which is put forward with a proof of its existence and finds the endogenous market shares and road congestion effects of SAV/HV. Original insights are obtained from model implementation, including substantial systemwide benefit of ridesharing, marginal benefit of relocation in the presence of ridesharing, and diminishing economies of SAV size.

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Transportation Research Part B: Methodological