A Batch Arrival Retrial Queue with Bernoulli Vacation Policy and Server Breakdown

Abstract

This paper examines the operating characteristics of an MX/G/1 retrial queueing system under Bernoulli vacation schedule with
setup times. The server renders first phase of essential service (FPS) to all the arriving units whereas second phase of multi-optional services (SPS) to only some of them who demand for the same. The server may breakdown according to Poisson process in working state i.e. either during FPS or SPS. The broken down server is then repaired by the repairman and becomes as good as before failure. When the server just after a service or repair completion finds no customers waiting to be served, he departs for a single vacation of arbitrary distributed length according to Bernoulli schedule. When the batch of arriving customers finds the server busy or on vacation, then the whole batch either with probability p joins a pool of blocked customers called ‘orbit’ or with complementary probability p (=1-p) leaves the system. On the other hand, if the arriving batch finds the server idle, then one of the customers
from the batch starts its service and the rest join the ‘orbit’. The service time, repair time, vacation time and setup time are assumed to be general distributed. Using supplementary variable technique and generating function method, the explicit expressions for the average system size, average orbit size and other performance indices have been determined.