• TRANSIENT SOLUTION OF M[X]/G/1 RETRIAL QUEUE WITH TWO STAGE HETEROGENEOUS SERVICE, EXTENDED VACATION, NON-PERSISTENT CUSTOMERS AND SETUP TIME

Abstract

This paper investigates a single server retrial queuing system with two stages heterogeneous service.Customers arrive in batches in accordance with compound Poisson processes. After the completion of first stage service, the second stage service starts with probability 1. In addition to this, the server takes Bernoulli vacation and setup times. We assume that the retrial time, the service time, the repair time, the vacation time and the setup time of the server are all arbitrarily distributed. We obtain the time dependent probability generating functions in terms of their Laplace transforms and the corresponding steady state results explicitly. Also we derive the average number of customers in the queue and the average waiting time in closed form with numerical illustration.