Queuing model of a traffic bottleneck with bimodal arrival rate

Kurzfassung

This paper revisits the problem of tuning the density in a traffic bottleneck by reduction of the arrival rate when the queue length exceeds a certain threshold, studied recently for variants of totally asymmetric simple exclusion process (TASEP) and Burgers equation. In the present approach, a simple finite queuing system is considered and its contrasting “phase diagram” is derived. One can observe one jammed region, one low-density region and one region where the queue length is equilibrated around the threshold. Despite the simplicity of the model the physics is in accordance with the previous approach: The density is tuned at the threshold if the exit rate lies in between the two arrival rates.