Highlights • A dynamic and aggregated non-equilibrium ride-sourcing model is developed to track the time-varying number of riders, vacant and occupied ride-sourcing vehicles. • The drivers are modeled as earning-sensitive, independent contractor, and self-scheduling and the riders are considered price- and quality of service-sensitive. • Supply and demand of the ride-sourcing market are endogenously modeled based on the fare requested from the riders and the wage paid to the drivers and the rider’s waiting time and driver’s cruising time. • A controller based on the MPC approach is proposed to dynamically control the fare and the wage. The MPC framework consists of two different models for plant and optimization. • The proposed model and controller enable the ride-sourcing provider to offer a wage to the drivers that is higher than the charged fare from the riders such that the overall profit is maximized.

Abstract Ride-sourcing is a prominent transportation mode because of its cost-effectiveness and convenience. It provides an on-demand mobility platform that acts as a two-sided market by matching riders with drivers. The conventional models of ride-sourcing systems are equilibrium-based, discrete, and suitable for strategic decisions. This steady-state approach is not suitable for operational decision-making where there is noticeable variation in the state of the system, denying the market enough time to balance back into equilibrium. We introduce a dynamic non-equilibrium ride-sourcing model that tracks the time-varying number of riders, vacant ride-sourcing vehicles, and occupied ride-sourcing vehicles. The drivers are modeled as earning-sensitive, independent contractor, and self-scheduling and the riders are considered price- and quality of service-sensitive such that the supply and demand of the ride-sourcing market are endogenously dependent on (i) the fare requested from the riders and the wage paid to the drivers and (ii) the rider’s waiting time and driver’s cruising time. The model enables investigating how the dynamic wage and fare set by the ride-sourcing service provider affect supply, demand, and states of the market such as average waiting and search time especially when drivers can freely choose their work shifts. Furthermore, we propose a controller based on the model predictive control approach to maximize the service provider’s profit by controlling the fare requested from riders and the wage offered to drivers to satisfy a certain quality of market performance. We assess three pricing strategies where the fare and wage are (i) time-varying and unconstrained, (ii) time-varying and constrained so that the fare is higher than the wage such that the instantaneous profit is positive, and (iii) time-invariant and fixed. The proposed model and controller enable the ride-sourcing service provider to offer a wage to the drivers that is higher than the fare requested from the riders. The result demonstrates that this myopic loss can potentially lead to higher overall profit when customer demand (i.e., riders who may opt to use the ride-sourcing system) increases while the supply of ride-sourcing vehicles decreases simultaneously.