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Paper details
Number 4 - December 2018
Volume 28 - 2018
From exhaustive vacation queues to preemptive priority queues with general interarrival times
Dieter Fiems, Stijn De Vuyst
Abstract
We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.
Keywords
queueing system, preemptive priority, server interruption, server breakdown, exhaustive vacations