International Journal of applied mathematics and computer science

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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

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.

queueing system, preemptive priority, server interruption, server breakdown, exhaustive vacations