MX/G/1 unreliable retrial queue with option of additional service and Bernoulli vacation

Abstract

In this paper, retrial queue with unreliable server and bulk arrivals is investigated. The server is capable of providing m-optional services and any one of these available services, may be rendered to the customer after the first essential service if the customer opts for the same. It is assumed that the server may fail while rendering any phase of service and undergoes for the immediate repair. After the completion of the service of a customer, the server may either take a vacation for a random period or may continue to provide the service to the other customers waiting in the queue. The supplementary variables corresponding to service time, repair time and retrial time are incorporated to determine the queue size distribution. To examine the effect of different parameters on the performance measures of the system, the numerical illustration is given which is supported by numerical simulation and sensitivity analysis.