International Journal of Combined Research pISSN:2321-2241 Volume: 3; Issue: 4; October–2014

This paper studies a batch arrival single server Bernoulli feedback queue with Poisson arrivals, two stages of heterogeneous service with different (arbitrary) service time distributions subject to random breakdowns and multiple vacations with exponential distributed with Mean vacation time . After first-stage service the server must provide the second stage service. However after the completion of two stage of service, if the customer is dissatisfied with his service or if he received unsuccessful service, then the customer may immediately join the tail of the original queue with probability p (0 ≤ p < 1) to receive first stage of service. Otherwise the customer may depart forever from the system with probability q = (1−p). The server takes vacation each time when the system becomes empty. On returning from vacation if the server finds no customer waiting in the system, then the server again goes for vacation until he finds at least one customer in the system. The system may breakdown at random and repair time follow exponential distribution. The time dependent probability generating functions has 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 average waiting time are derived. The probability generating function of queue size at a random epoch is obtained. Particular cases and some special cases are discussed. Numerical illustration for particular values of parameters is presented.