Simulation of Traffic Flow between Signals by the Continuum Model

Abstract

The continuum model of traffic flow has been used in the analysis of the traffic flow on highways. In this paper this model is applied to the traffic flow controlled by signals on urban streets. First, the basic nonlinear equation which governs the traffic flow is derived, then it is transformed to a heat conduction equation under a suitable nonlinear transformation.
On a one-way road, we consider a section between two traffic signals which have a common cycle time. In a steady state, the traffic density distribution changes periodically. For calculating this periodic distribution an algorithm is proposed, where the input flow at the first signal and the parameter values of the second signal are assumed to be given. In the algorithm an initial-boundary value problem of the heat conduction equation is repeatedly solved. By comparing the distributions obtained for the various offset values, the optimal offset is determined. Some numerical examples are also shown.