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.
Ayyappan, G. and Thamizhselvi, P.
Priority Queueing System with a Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 with Balking and Optional Server Vacation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
1, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss1/3