Strategic customer behavior in a queueing system with a loss subsystem

We study a non-cooperative multi-player game of rational customers in a queueing network composed of two unobservable single-server subsystems with different regimes. The first subsystem is a free-shared first-come first-served queue with waiting time affected by congestion. Wishing to avoid congestion, customers may choose to turn to the second subsystem that offers service with no delay. However, reaching the second server is costly and can go unrewarded because requests are blocked when the server is busy. Still, blocked customers do not leave the system empty-handed—they are instantaneously rerouted to the shared queue at the first server. The decision and benefit of each customer depend on the choices of the others, bringing about a symmetric non-cooperative game. After analyzing the queueing characteristics of the system, we show, by properties of the cost function, that a unique symmetric Nash equilibrium exists. Comparing the equilibrium strategy with the socially optimal strategy, we find that, contrary to intuition, customers may choose the loss system more, less or in an equal proportion to what is socially preferred.