Analysis of Priority Queueing System with Working Breakdown,Vacation and Vacation Interruption under Random Environment

study priority queueing system consisting of working breakdown, repair, single vacation and vacation interruption. At a breakdown instant during the busy period, without stop the servie, the server provides service at slower rate for the current customer. After completion of priority service, depending on the environment, the server can choose type I or type II vacation. Both types of vacation are considered as a single vacation. On completion of type I vacation if the server finds thepriority queue is empty, he has the option to take type II vacation. During the type II vacation, when priority customers arrive the server has the option to interrupt the vacation. We use the established norm which is the corresponding steady state results for time dependent probability generating functions are obtained. Along with that, the expected waiting time for theexpected number of customers for both high and low priority queues are computed. Numerical results along with the graphical representations are shown elaborately

Priority Queueing System with a Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 with Balking and Optional Server Vacation

In this paper we study a vacation queueing system with a single server simultaneously dealing with an M[x1] /G1/1 and an M[x2] /G2/1 queues. Two classes of units, priority and non-priority, arrive at the system in two independent compound Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority and non-priority units. We further assume that the server may take a vacation of random length just after serving the last customer in the priority unit present in the system. If the server is busy or on vacation, an arriving non-priority customer either join the queue with probability b or balks(does not join the queue) with probability (1 - b). The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained explicitly. Also the average number of customer in the priority and the non-priority queue and the average waiting time are derived. Numerical results are computed