Particle hopping models and traffic flow theory

This paper shows connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equation, and particle hopping models, and starts building a foundation of a comprehensive dynamic traffic theory, where strengths and weaknesses of different models can be compared, and thus allowing to systematically choose the appropriate model for a given question.

Abstract

This paper shows how particle hopping models fit into the context of traffic\nflow theory. Connections between fluid-dynamical traffic flow models, which\nderive from the Navier-Stokes-equations, and particle hopping models are shown.\nIn some cases, these connections are exact and have long been established, but\nhave never been viewed in the context of traffic theory. In other cases,\ncritical behavior of traffic jam clusters can be compared to instabilities in\nthe partial differential equations. Finally, it is shown how this leads to a\nconsistent picture of traffic jam dynamics.\n