Complementarity models for traffic equilibrium with ridesharing

•A new traffic equilibrium model with ridesharing is proposed.•It determines how travelers will behave given ridesharing and traffic conditions.•Mixed complementarity problem and variational inequality formulations are described.•The conditions for the existence and uniqueness are provided and proved.

It is estimated that 76% of commuters are driving to work alone while each of them experiences a 38-h delay annually due to traffic congestion. Ridesharing is an efficient way to utilize the unused capacity and help with congestion reduction, and it has recently become more and more popular due to new communication technologies. Understanding the complex relations between ridesharing and traffic congestion is a critical step in the evaluation of a ridesharing enterprise or of the effectiveness of regulatory policies or incentives to promote ridesharing. The objective of this paper is to introduce a mathematical framework for the study of the ridesharing impacts on traffic congestion and to pave the way for the analysis of how people can be motivated to participate in ridesharing, and conversely, how congestion influences ridesharing activities. We accomplish this objective by developing a new traffic equilibrium model with ridesharing, and formulating the model as a mixed complementarity problem (MiCP). We provide conditions on the model parameters under which there exists one and only one solution to this model. The computational results show that when the congestion cost decreases or the ridesharing inconvenience cost increases, more travelers would become solo drivers and thus less people would participate in ridesharing. On the other hand, when the ridesharing price increases, more travelers would become ridesharing drivers.