Stochastic noise approach to traffic flow modeling

Traffic flow states are described as resulting from a stochastically driven system. Vehicles advance based on the energy profile of their surrounding traffic. We create a stochastic process generated from an ergodicity satisfying Markov chain whose system dynamics sample from the Gibbs distribution. Specifically, we employ Arrhenius microscopic dynamics in order to also capture non-equilibrium behavior and monitor the states favored by the system through its time evolution. Monte Carlo simulations of this traffic system provide information and statistics regarding free-flow, “synchronized” traffic, jam wave formation or dissipation, “stop and go” regimes and a variety of interesting such traffic behavior, summarized in, among others, the fundamental diagram. Generalizations to the current model and a number of ideas for further studies are proposed.