Exact Solutions for a Discrete System Arising in Traffic Flow

Abstract

This paper concerns wave propagation in a discrete nonlinear system of equations proposed and studied by G. F. Newell as a model for car-following in traffic flow. In particular, Newell found exact solutions for shock waves and related phenomena. Here, exact solutions representing periodic waves and solitary waves are obtained. The method relates travelling wave solutions to the Toda and Kac-van-Moerbeke discrete systems. In this and other ways, much of the interest is in the general phenomena possible in discrete systems, here including also a time lag, rather than in just the specific traffic flow setting.