Bulletin of Pure & Applied Sciences- Mathematics and Statistics

In this paper, we consider a single server queuing system with two types of batch arrivals and services under non preemptive priority rule. Arrivals follow a compound Poisson process. The server provides single service to the high priority customers and the general bulk service rule for the low priority customers on a FCFS discipline. The server starts service to the low priority customers only if the high priority queue is empty and the number of customers in the low priority queue is greater than or equal to ‘a’. If there are no customer in the high priority queue and the number of customers in the the low priority queue are less than ‘a’ then the server becomes idle. The service time for each service follows a general(arbitrary) distribution. Using the supplementary variable technique, the time dependent probability generating functions of the distributions P_{m, n}, q_{m, n} and P_{m, n}⁺, q_{m, n}⁺ under equilibrium, have been derived in terms of their Laplace transforms and the corresponding steady state results are also derived. The average number of customers in the queues and the average waiting time are derived. Numerical case has been worked out on the assumption that the service time follows a specified exponential and Erlang-2 distributions.