A general equilibrium model for transportation systems with e-hailing services and flow congestion

•e-HSP choices, customer choices, and network congestion are three essential modules for e-hailing services.•General equilibrium model can be used to capture the behavior/interactions of the three modules.•Customer/vehicle waiting times are modeled endogenously and separately.•The usage of different services depends on key model parameters relate to e-HSP/customers.•Network effect is closely related to the overall e-HSP usage and the symmetry of travel demands. Passengers are increasingly using e-hailing as a means to request transportation services. Adoption of these types of services has the potential to impact the travel behavior of individuals as well as increase congestion and vehicle miles driven since extra deadhead miles must be added to the trip (e.g., the extra miles from the driver location to the pick-up location of the customer). The objective of this paper is to develop a basic mathematical model to help transportation planners understand the relationship between the wide-scale use of e-hailing transportation services and deadhead miles and resulting impact on congestion. Specifically, this paper develops a general economic equilibrium model at the macroscopic level to describe the equilibrium state of a transportation system composed of solo drivers and the e-hailing service providers (e-HSPs). The equilibrium model consists of three interacting sub-models: e-HSP choice, customer choice, and network congestion; the model is completed with a “market clearance” condition describing the waiting costs in the customer’s optimization problem in terms of the e-HSPs’ decisions, thereby connecting the supply and demand sides of the equilibrium. We show the existence of an equilibrium of a certain kind under some mild assumptions. In numerical experiments, we illustrate the sensitivity on the usage of these modes to various parameters representing cost, value of time, safety, and comfort level, as well as the resulting relationship between usage of these services and vehicle miles.