Congestion and departure time choice equilibrium in urban road networks

When drivers are regularly faced with congestion, they try to optimize their departure time. If the demand and the road network evolve slowly enough, the entire system may approach an equilibrium, i.e. a state such that no one can be better off by unilaterally changing departure time. The transportation community has devoted a significant effort to identify such equilibria. The ultimate goal is to be able to predict the consequences of large infrastructure projects and to design smart policies to alleviate congestion. Yet, several issues still limit the applicability of the existing literature. This thesis identifies three complementary challenges and attempts to address them.

We first investigate whether, from a theoretical viewpoint, real world unidirectional flows are likely to be in a near-equilibrium state. Our analytical findings reveal the influence of schedule preferences on stability, and explain why morning commutes are more likely to be unstable than evening ones. Fortunately, user heterogeneity or socially optimal pricing can soften the effects of instability. Residual oscillations result in a congestion cost decomposition that differs from the one observed at equilibrium, but the overall average congestion cost at equilibrium is remarkably accurate.

We then characterize departure time choice equilibria in isotropic regions, representing multi-directional road networks. In this context, users can slow down others who started their trips earlier and trip length is an important determinant of departure time choice. We show that with a widely used type of schedule preferences, users with long trips tend to avoid the peak period. Although the First-In, First-Out (FIFO) property does not hold in general with heterogeneous trip lengths, such a pattern emerges among families of early and late users having the same preferences. Simulations suggest that the social cost and its decomposition greatly differ from those observed in unidirectional settings.

We finally propose an alternative way of reducing congestion, based on an optional booking service with dedicated right-of-way. Such a service would be advantageously implemented with shared and/or autonomous vehicles, due to similar requirements and complementarity. We recognize that participation to such a program would entail an alternative-specific inconvenience and evaluate the consequences on welfare depending on the way it is administrated and on the capacity split.

Overall, this thesis advances the state of knowledge regarding the prevailing traffic conditions and suggests ways to improve them. The adopted approach is largely analytical to provide insight and generality. Complementary simulations add realism and push back the limits of tractability.