Analysis of customer's impatience on bulk service queueing system with unreliable server, setup time and two types of multiple vacations

Abstract

In this investigation, we analyse the customer's impatience on unreliable bulk queueing system with two types of vacation. Depending upon the length of queue, the server is permitted to take two types of vacation called type I vacation and type II vacation. The server is possibly affected by breakdowns and takes considerable time for setup before the repair begins to start. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. It could be assumed that the arriving units may be balked from the system when the server is on vacation (type I or type II). By incorporating the supplementary variables technique, the probability generating function of the queue size at an arbitrary and departure time epoch for the designed queueing system are derived. Finally, the stability condition, some performance measures, particular cases are obtained with appropriate numerical illustrations and graphical presentation.