Congestion Control for a System with Parallel Stations and Homogeneous Customers Using Priority Passes

We consider a game theoretic congestion model with parallel nodes and homogeneous customers. The purpose of this paper is to examine how the priority passes improve social welfare for such a system. To this end, we prove the existence of an equilibrium. The system with no priority pass has a unique equilibrium. With the introduction of priority passes, the uniqueness of the equilibrium may be destroyed. We provide a sufficient condition under which the system with priority passes outperforms the system with no priority passes. The problem is explored numerically as well.