A User Equilibrium Model for a Dynamic Ridesharing Market

Abstract

Over the past decade, advances in mobile communication technology and global positioning systems have enabled the implementation of dynamic ridesharing, which is considered a promising approach to reducing travel cost, alleviating traffic congestion, and decreasing greenhouse gas emissions. Unlike pre-arranged scenarios, dynamic ridesharing allows drivers and riders to make requests dynamically and be matched on short notice or even en-route, making it well-suited for on-demand requests. Predicting the traffic pattern of drivers under a dynamic ridesharing market is a critical step in evaluating ridesharing platforms and the efficacy of regulatory policies or incentives aimed at promoting ridesharing. In this paper, we take the first attempt to establish a user equilibrium model under a dynamic ridesharing market to investigate the route choices of drivers, where private car owners are assumed to select the route with the highest pairing probability to satisfy their travel needs. The intricate competition and pairing relationships between riders' and drivers' OD pairs pose a challenging task. To disentangle the complex interactions among OD pairs, different waiting-states and seeking-states are constructed for each OD pair, and the pairing relationships between these states are well-defined. With these relationships, a system of nonlinear equations is established to describe the user equilibrium under a dynamic ridesharing system. By constructing a sequence of fixed-point problems, the existence of an equilibrium solution is guaranteed. An alternating optimization algorithm is then devised to solve this problem, incorporating dynamic programming to find the feasible route with the highest pairing probability for each driver-OD pair. The effectiveness of this algorithm is demonstrated on several large-scale road networks.

Keywords: Dynamic ridesharing, User equilibrium, Traffic assignment