An analysis of the equilibrium strategies for route-choosing customers in a two-station queueing system

Abstract

We investigate a two-station queueing system where strategic customers must be sequentially serviced at both stations. We prove that an established property—that the distribution of the total time spent in a two-station system is independent of the chosen route when services times are exponentially distributed—is not a general one by providing a counterexample with deterministic service times. In doing so, we also prove a concomitant property—that any routing strategy is an equilibrium—is peculiar to the system with the particular assumption of the exponential service time distribution. Using simulations, we show that—depending on the distribution of service times—there can be (1) cases with three equilibria, (2) a case with a unique pure strategy equilibrium, and (3) cases with a unique mixed strategy equilibrium.