On the Equilibrium and Stability Properties of a Macroscopic Model for Ride-Hailing Services with Limited Fleet Size

With the growing popularity of ride-hailing services and the desire to operate those services efficiently, ridehailing companies need to ensure a sufficiently large fleet size and an appropriate rebalancing of empty vehicles. Due to the complexity of city traffic dynamics, macroscopic modeling approaches are often required. In this work, we present a macroscopic compartment model for ride-hailing services and characterize its equilibrium properties. If the service is only operating in one region, we provide both sufficient and necessary conditions for the system to converge to a unique equilibrium. If the service is operating over a couple of regions, we provide the necessary conditions for the request queues to stay bounded. When operating over more than one region, there is a need for a rebalancing controller for sending idling vehicles to another region. Hence, we present a Model Predictive Control (MPC) approach to solve the rebalancing problem and compare its performance with some simpler myopic controllers.