Time Dependence in Commuter Traffic Models

In this paper we formulate a basic model for two-dimensional time-dependent traffic flow. The model is designed specifically to relate to the morning peak period of commuter traffic, for which the underlying ideas are relatively unencumbered. The time variation of the point value of the “travel intensity at a given time point” is considered and also the global “wave movement” that peak hour traffic will exhibit—the peak hour will not be entirely synchronous at all points over the city. It is found that under standard assumptions as to routing and the location of trip end points, a strong peak hour occurs in the form of a shock wave. The effect of changes to the routing system and trip-end distribution is also considered.