Influence of dynamic congestion with scheduling preferences on carpooling matching with heterogeneous users

Carpooling is an efficient measure to fight car ownership and reduce vehicle kilometres travelled. By individuals sharing their commutes, vehicle occupancy increases and congestion is reduced. We develop a dynamic ADL (Arnott, de Palma, Lindsey)-Vickrey approach for a corridor monocentric city a la Hotelling. First, we formulate the matching problem of heterogeneous users in carpooling as an MILP problem and we discuss its analytical properties when there is no congestion. Next, we construct a bi-level optimization problem involving matching (first stage) and dynamic traffic congestion with scheduling preferences (second stage) when congestion is endogenous. We provide a heuristic to attain an optimal matching for a dynamic traffic equilibrium with congestion. Such a template allows studying the two-way causality between dynamic congestion and carpooling matching.