Urban Mobility Redefined: Stochastic Equilibrium and Optimal Car Ownership in Cities With Ridesharing Programs

Ridesharing programs, as a new form of shared mobility, offer opportunities to build a more efficient and sustainable society. This paper first examines the mode choices of travelers in cities where ridesharing services are available. Specifically, travelers choose among four modes: solo drivers, ridesharing drivers, ridesharing riders, and public transit riders. To capture the mode choice behaviors of travelers, we build a stochastic ridesharing user equilibrium (SRUE) model with heterogeneous travelers in terms of car ownership. However, because of the inseparability of cost functions along with asymmetry in link interactions, the stochastic ridesharing user equilibrium is formulated as a variational inequality (VI) problem and an equivalent mixed complementarity problem (MiCP). Moreover, we prove the existence and uniqueness of the solution of SRUE under certain conditions. Besides, to address the decision-making problem of optimal car ownership in cities with ridesharing programs, we establish a bilevel optimization model that determines the optimal car ownership at the upper level and the equilibrium traffic flow solution at the lower level. Then, it is reformulated and solved as a mathematical problem with complementarity constraints (MPCC). Finally, numerical experiments are conducted to demonstrate our results and optimal car ownership in different scenarios.