Dynamic equilibrium analyses in a ride-sourcing market under travel time uncertainty

Abstract

This paper proposes a dynamic equilibrium framework for the morning commute problem in the ride-sourcing market under travel time uncertainty. It is formulated as a simultaneous departure time and mode choice problem (SDTMCP) with random travel delay. Commuters are considered to choose among four travel modes: (1) driving alone, (2) taking non-shared service, (3) taking ride-sharing service, and (4) taking the metro. The equilibrium state is reached when no commuter can reduce their expected travel cost by unilaterally changing their mode or departure time. We derive the dynamic equilibrium queuing patterns analytically under certain assumptions, and develop an approach using nonlinear complementarity problem (NCP) to solve general problems where analytical results cannot be readily derived. We further explore the pricing strategy of the ride-sourcing platform, in which travel time uncertainty and the prices of ride-sourcing services jointly determine the profit performance. A mathematical program with equilibrium constraints (MPEC) is formulated to search for the optimal service prices to achieve the maximum profit. The framework is then extended to investigate the pricing strategy in a two-sided ride-sourcing market and examine the metro crowdedness effect in the numerical studies.