Coordinating Dynamical Routes with Statistical Physics on Space-time Networks

Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static or without inter-vehicle coordination. In this paper, we first apply the cavity approach in statistical physics to derive the theoretical behavior and an optimization algorithm for dynamical route coordination, but they become computational intractable as the number of time segments increases. We therefore map static spatial networks to space-time networks to derive a computational feasible message-passing algorithm compatible with arbitrary system parameters; it agrees well with the analytical and algorithmic results of conventional cavity approach and outperforms multi-start greedy search in saving total travel time by as much as 15% in simulations. The study sheds light on the design of dynamical route coordination protocols, and the solution to other dynamical problems via static analytical approaches on space-time networks.