Equilibrium Strategies for Overtaking-Free Queueing Networks under Partial Information

In this paper, we investigate the equilibrium strategies for customers arriving at overtaking-free queueing networks and receiving partial information about the system’s state. In an overtaking-free network, customers cannot be overtaken by others arriving after them. We assume that customer arrivals follow a Poisson process and that service times at any queue are independent and exponentially distributed. Upon arrival, the received partial information consists in the total number of customers already in the network, however the distribution of these among the queues is left unknown. We prove the existence of equilibrium threshold strategies for such systems and provide methods to compute them.