Priority queues with semi-exhaustive service

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 queue n until the number of messages decreases to one less than that found upon the server's last arrival at queue n, where 1 less than or equal to n less than or equal to 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.