Time Dependent Solution of Batch Arrival Queue with Second Optional Service, Optional Re-Service and Bernoulli Vacation

Abstract

This paper deals with an M[X]/G/1 queues with second optional service, optional re-service and Bernoulli vacations. Each customer undergoes first phase of service after completion of service, customer has the option to repeat or not to repeat the first phase of service and leave the system without taking the second phase or take the second phase service. Similarly after the second phase service he has yet another option to repeat or not to repeat the second phase service. After each service completion, the server may take a vacation with probability 1-theta or may continue staying in the system with probability . The service and vacation periods are assumed to be general. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Also the average number of customers in the queue and the waiting time are also derived.

Keywords: Batch arrival, Second optional service, Optional re-service, Average queue size, Average waiting time.