Author(s)

Kailash C. Madan

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We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.

Non Preemptive Priority Queueing System, Modified Server Vacations, Combination of General Service and Deterministic Service, Steady State, Queue Size Distribution

K. Madan, "A Non-Preemptive Priority Queueing System with a Single Server Serving Two Queues M/G/1 and M/D/1 with Optional Server Vacations Based on Exhaustive Service of the Priority Units," Applied Mathematics, Vol. 2 No. 6, 2011, pp. 791-799. doi: 10.4236/am.2011.26106.