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