A retrial queue with server interruptions, resumption and restart of service

Abstract

This paper analyses a single server retrial queuing model with service interruptions, resumption/restart of interrupted service. The service is assumed to get interrupted according to a Poisson process. The interrupted service is either resumed or restarted according to the realization of two competing independent, non-identically distributed random variables, the realization times of which follow exponential distributions. Arrival of primary customers constitutes a Poisson process. On arrival if a customer finds an idle server, he is immediately taken for service. If the server is busy when a customer arrives, this customer goes to an orbit of infinite capacity from where he makes repeated attempts for service according to a Poisson process with parameter β. After an unsuccessful retrial he rejoins the orbit with probability p and leaves the system without waiting for service with probability q = 1 − p. The service time durations follow PH distribution with representation (α, S) of order m, when there is no interruption. The system is found to be always stable if q > 0. The case q = 0 is also analyzed. Using Matrix analytic method, expressions for important system characteristics such as expected service time, expected number of interruptions are obtained. System performance measures are numerically explored and the effect of service interruptions in a retrial set up is studied.