Hyperbolic PDE modeling traffic flow in terms of macroscopic quantities (like density) describe dynamics for an aggregate traffic flow. However, we understand the nature of traffic flow is such that any driver may have a significant impact on the flow. We also know that drivers are not completely consistent with each other or themselves over time; their dynamics include continuous variation around a mean behavior. An approach for integrating stochastic variation into existing macroscopic traffic models through the introduction of a small parameter governed by a stochastic heat equation and a parameterized family of equilibrium behaviors (fundamental diagrams) is presented. Utilizing this model we show spontaneous generation of traffic jams qualitatively consistent with experimental behavior.
Speaker(s): John Wakefield (University of Michigan)