Three-Stream Model for Arterial Traffic

In this article, a new analytical traffic flow model is proposed for traffic dynamics at signalized intersections. During each cycle, both the arrival and the departure traffic are approximated by three distinct traffic streams with uniform density. Because of the similar representation of the arrival and the departure traffic, results from a single intersection can easily be extended to a series of intersections. With this model, the number of parameters of the model is tractable, leading to analytical solutions of the problem. It also is proved that the total delay of one-way traffic is a quasi-convex function in the offset between consecutive traffic cycles. The optimal signal control can be analytically derived under different scenarios, which allows timely adjustments of the control as congestion evolves throughout the day. How different scenarios evolve in a corridor, from one intersection to the downstream one, if there is no traffic from/to side streets, is also studied. All scenarios eventually lead to one scenario after a few intersections. This scenario corresponds to a green wave, which is shown to be in agreement with physical intuition. Finally, the model is tested against data from microsimulation using CORSIM. Vehicle delay predicted by the model is shown to be close to that from the microsimulation.