A general coupled morning–evening traffic equilibrium model with rideshare, ride-hailing, and public transit services

We develop a general equilibrium model to capture the complex interactions between different modes, such as solo driving, public transit, as well as rideshare and ride-hailing services such as Uber and Lyft, under a joint morning and evening commute framework. Formulated as a variational inequality (VI) and equivalently as a mixed complementarity problem (MiCP), the model allows (a) travelers to switch between different transportation modes and (b) passengers from different Origin-Destination (OD) pairs to share a ride together. The computational results on the Sioux-Falls network show that our model captures the possible mode switches and the coupling effects between morning and evening commutes. Furthermore, our numerical examples demonstrate that modelling morning and evening commutes separately tends to overestimate the travelers' disutility and the average Vehicle Miles Traveled (VMT) in the network.