General stochastic ridesharing user equilibrium problem with elastic demand

Abstract

In this study, we propose a general stochastic ridesharing user equilibrium (SRUE) problem with elastic demand (ED) for urban transportation network analysis with ridesharing activities by extending the deterministic ridesharing user equilibrium (DRUE) problem, which is referred to as the general SRUE-ED problem. We develop a novel variational inequality (VI) model in terms of the Lagrange multipliers corresponding to the ride-matching constraints for the general SRUE-ED problem. The existence and uniqueness of the SRUE-ED solution are demonstrated under mild conditions. We proceed to put up a global convergent method to solve the developed VI model by incorporating the weighted cost averaging (WCA) method. The purpose of WCA method is to solve a parametric fixed-point model formulated for the general SRUE-ED problem without the ride-matching constraints. Finally, we use three numerical examples to provide practical insights into the operation and management of the ridesharing systems and to examine the effectiveness of the proposed model and solution method.