WHAT DOES THE ENTROPY CONDITION MEAN IN TRAFFIC FLOW THEORY

Mathematical models of freeway traffic flow do not include models of the driver's ride impulse (e.g. of the fact that drivers really start if a traffic light switches form red to green). Moreover, the occurrence of shocks leads to the necessity to deal with weak solutions of mathematical models, as far as models formulated in terms of conservation laws are concerned. But the transition from a classic conservation law differential equation to its weak formulation leads to a loss of uniqueness of the solution. This also happes in gas dynamics where an entropy condition was additionally introduced in order to pick out the physically true solution. In this paper, it will be pointed out that this entropy condition can also be used in traffic flow theory as a uniqueness criterion, and that it is - strangely enough - the missing mathematical model of the ride impulse. These ideas are exemplified in case of the Lighthill-Whitham model which so seems to become again an up-to-date model that can numerically be treated by means of very effective numerical procedures such as TVD methods. © 1990.