Equilibrium Customer Strategies in the Single-Server Constant Retrial Queue with Breakdowns and Repairs

TLDR: Nash equilibrium analysis for customers’ joining strategies as well as the related social and profit maximization problems is investigated and the effect of the information levels and several parameters on the customers�’ equilibrium and optimal strategies is presented.

Abstract: We consider a single-server constant retrial queueing system with a Poisson arrival process and exponential service and retrial times, in which the server may break down when it is working. The lifetime of the server is assumed to be exponentially distributed and once the server breaks down, it will be sent for repair immediately and the repair time is also exponentially distributed. There is no waiting space in front of the server and arriving customers decide whether to enter the retrial orbit or to balk depending on the available information they get upon arrival. In the paper, Nash equilibrium analysis for customers’ joining strategies as well as the related social and profit maximization problems is investigated. We consider separately the partially observable case where an arriving customer knows the state of the server but does not observe the exact number of customers waiting for service and the fully observable case where customer gets informed not only about the state of the server but also about the exact number of customers in the orbit. Some numerical examples are presented to illustrate the effect of the information levels and several parameters on the customers’ equilibrium and optimal strategies.