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•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, the paper derives 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. It also derives a conversion relationship between the LSTs for waiting times in the multiple and single vacation models.
