Traffic Flow States in a Freeway with Bottle neck

The system of mixture of single lane and double lane is studied by a cellular automata model, which is developed by us based on the Nagel and Schreckenberg's models.We justify that the model can reach a stable states quickly. The density distributions of the stable state is presented for several cases, which illustrate the manner of the congestion. The relationship between the outflow rate and the total number of vehicles and that between the outflow rate and the density just before the bottleneck are both given. Comparing with the relationship that occurring in the granular flow,we conclude that the transition from the free traffic flow to the congested traffic flow can also be attributed to the abrupt variation through unstable flow state, which can naturally explain the discontinuities and the complex time variation behavior observed in the traffic flow experiments.