On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations

Abstract

A single-server retrial queue with two types of customers in whichthe server is subject to vacations along with breakdowns and repairs is studied. Twotypes of customers arrive to the system in accordance with twodifferent independent Poisson flows. The service times of the two types ofcustomers have two different independent general distributions. We assume that when a service iscompleted, the server will take vacations after an exponentiallydistributed reserved time. Itis assumed that the server has an exponentially distributedlifetime, a generally distributed vacation time and a generallydistributed repair time. There is no waiting space infront of the server, therefore, if the server is found busy, or onvacation, or down, the blocked two types of customers form twosources of repeated customers. Explicit expressions are derived for theexpected number of retrial customers of each type. Additionally, byassuming both types of customers face linear costs for waiting andretrial, we discuss and compare the optimal and equilibrium retrialrates regarding the situations in which the customers arecooperative or noncooperative, respectively.