On optimal and equilibrium retrial rates in an unreliable retrial queue with two types of customers

A single-server retrial queue with two types of customers in which the server is subject to breakdowns and repairs is studied. Two types of customers arrive to the system in accordance with two different independent Poisson flows. There is no waiting space in front of the server and therefore, if the server is found busy or down, the blocked two types of customers form two sources of repeated calls. The service times of the two types of customers have two different independent general distributions. It is also assumed that the server has a service-type dependent exponentially distributed lifetime as well as a service-type dependent, generally distributed repair time. Explicit expressions are derived for the expected number of retrial customers of each type. In addition, by assuming both types of customers face linear costs for waiting and conducting retrials, we discuss and compare optimal and equilibrium retrial rates respectively regarding the situations in which the customers are cooperative or noncooperative.