A single server retrial queue with event-dependent arrival rates

Abstract

In this work, we consider a novel single-server retrial queue with event-dependent arrival rates. Contrary to other related works, the primary customers’ arrival rates depend on the last realized event, which refers either to a departure, or to an arrival of either type, or to when a customer arrives during a busy period, compared with others. Our motivation stems from the modeling of service systems, in which the customers express their willingness to join the system based on the last realized event. We investigate the stability conditions, and derive the stationary distribution both at service completion epochs, and at an arbitrary epoch. We also study the asymptotic behaviour under high rate of retrials. Performance measures are explicitly derived, and extensive numerical examples are performed to investigate the impact of event-dependency. Moreover, constrained optimisation problems are formulated and solved with ultimate goal to derive optimal joining probabilities.