Abstract
This paper studies a new type of multi-class priority queues with semi-exhaustive service and server vacations, which operates as follows: A single server continues serving messages in queuen until the number of messages decreases toone less than that found upon the server's last arrival at queuen, where 1≤n≤N. In succession, messages of the highest class present in the system, if any, will be served according to this semi-exhaustive service. Applying the delay cycle analysis and introducing a super-message composed of messages served in a busy period, we derive explicitly the Laplace-Stieltjes transforms (LSTs) and the first two moments of the message waiting time distributions for each class in the M/G/1-type priority queues with multiple and single vacations. We also derive a conversion relationship between the LSTs for waiting times in the multiple and single vacation models.
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Katayama, T. Priority queues with semi-exhaustive service. Queueing Syst 21, 161–181 (1995). https://doi.org/10.1007/BF01158579
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DOI: https://doi.org/10.1007/BF01158579