Steady state analysis of the GI/M/1/N queue with a variant of multiple working vacations

This paper studies the GI/M/1/N queue with a variant of multiple working vacations, where the server leaves for a working vacation as soon as the system becomes empty. The server takes at most H consecutive working vacations if the system remains empty after the end of a working vacation. Employing the supplementary variable and embedded Markov chain methods, we obtain the queue length distribution at different time epochs. Based on the various system length distribution, the probability of blocking, mean waiting times and mean system lengths have been derived. Finally, numerical results are discussed.

► The GI/M/1/N queue with a variant of multiple working vacation.
► The queue length distribution at pre-arrival and arbitrary epochs.
► Several performance measures and special cases are discussed.