Path-Based Multi-Passenger Ridesharing User Equilibrium Model for a Large Network

Ridesharing has the potential to enable more efficient use of private vehicles and, therefore, to solve various transportation-related problems, such as traffic congestion and environmental pollution. Furthermore, the implementation of ridesharing will make private cars more convenient, which may cause a modal shift from public transportation to automobiles. Here, we introduce a logit-based stochastic ridesharing user equilibrium (RUE) model that can be solved even for a larger-sized network. In the proposed model, travelers have three options: as a rideshare driver (RD), who travels in their own vehicle to their destination while allowing for shared seating; a rider (R) who rides with an RD; and a public transportation user (PT), who takes public transportation to their destinations. The proposed model explicitly considers the en-route transfer-free condition of riders by generating a set of paths from a path of the RD. With some simplifying assumptions, the proposed model is formulated as the Beckmann transformation in the mathematical problem formulation, in which a unique solution is guaranteed. The solution algorithm that combines the column generation approach and the Lagrangian relaxation method was adopted. The proposed model was then applied to the Sioux Falls network to confirm the convergence process and model outputs, as well as to perform a parameter sensitivity analysis. Finally, to confirm the convergence process and model outputs, the proposed model was applied to the Anaheim network, as an example of a network of larger size than those represented by other models.