Level crossing analysis of priority queues and a conservation identity for vacation models

The two purposes of this article are to illustrate the power and simplicity of level crossing analysis and to present a conservation identity for M/G/1 priority queues with server vacations. To illustrate the use of level crossing analysis the paper applies it to preemptive (resume) priority M/G/1 queues with single- and multi-server vacations considered by Kella and Yechiali and to non-preemptive priority M/M/c queues considered by Kella and Yechiali. The conservation identity presented here states that the ratios of mean waiting times in a M/G/1 queue with and without server vacation policies are independent of the service discipline for first come first served, shortest processing time, shortest processing time within generations and non-preemptive priority service disciplines.