Abstract
In this paper considers M[X1]/G1/1, M[X2]/G2/1 , M[X3]/G3/1 general queueing system with priority services . Three types of customers from different classes arrive at the system in different independent Poisson process. The server follows the non preemptive priority rule subject to working breakdown, and modified Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there is no high priority customers present in the system. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained. Also the average number of customer in the priority and non priority, preemptive priority queue and the average waiting time are derived.
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