A Dynamic Model of the Two-Route Traffic Flow

So far, various traffic flow models have been developed for reproducing and explaining some complex traffic phenomena, e.g., stop-and-go traffic, phase transition, local cluster, traffic waves (shock wave, rarefaction wave, soliton wave and kink wave), lane-changing, overtaking and others. Most of these models are subject to the traffic on highways, rather than that on networks. On the other hand, the studies associated with networks mainly address the macro issues of traffic flows, for example, the modeling of route and departure time choices. These network models are difficult to explain the micro properties of traffic flows in a network. Therefore, it is interesting to develop a modeling approach which can considers the micro and macro points of traffic flow simultaneously. Some researchers have recently extended the kinematic model and cellular automata model to describe the network flow. The kinematic model doesn't take into account momentum equation and the cellular automata model is based on simulation. In this paper, we present a dynamic model to formulate the network flow. A simple network with two routes and one O-D pair is selected as the modeling object. Numerical results show that our model can well reproduce the evolution of the inflow, outflow and the flow on each link when a small perturbation of the arrival of private vehicles appears.