Abstract
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.
Highlights
Several authors including Cobham [1], Phipps [2], Schrage [3], Jaiswal [4], Madan [5], Simon [6], Takagi [7], Choi and Chang [8] have studied priority queues
We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue
We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system
Summary
Several authors including Cobham [1], Phipps [2], Schrage [3], Jaiswal [4], Madan [5], Simon [6], Takagi [7], Choi and Chang [8] have studied priority queues These authors and several others have studied single server or multi-server queues with two or more priority classes under preemptive or non-preemptive priority rules. Under the non-preemptive queue discipline, they assume that the service time V of a priority unit has a general distribution and that of a non–priority unit is deterministic Their model is a combination of the M/G/1 and M/D/1 queues and the server keeps switching over these two queues depending on the class of units present in the system. We generalize the results of Madan and Abu-Dayyeh [9], and some other known results of the M/G/1 and the M/D/1 queues as particular cases
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