Abstract
This paper studies batch arrival M X /G/1 priority queues without and with (multiple or single) vacations. Applying the delay busy cycle analysis, we explicity derive the Laplace-Stieltjes transforms and the first two moments of the waiting time distributions for the nonpreemptive (head-of-the-line) and preemptive resume priority queues. Conservation laws for batch arrival systems are also mentioned. The results in this paper cover many previous results as special cases.
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