On the stationary distribution of queue lengths in a multi-class priority queueing system with customer transfers

On the stationary distribution of queue lengths in a multi-class priority queueing system with customer transfers

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Article ID: iaor200971406
Country: Netherlands
Volume: 62
Issue: 3
Start Page Number: 255
End Page Number: 277
Publication Date: Jul 2009
Journal: Queueing Systems
Authors: , ,
Abstract:

This paper deals with a multi-class priority queueing system with customer transfers that occur only from lower priority queues to higher priority queues. Conditions for the queueing system to be stable/unstable are obtained. An auxiliary queueing system is introduced, for which an explicit product-form solution is found for the stationary distribution of queue lengths. Sample path relationships between the queue lengths in the original queueing system and the auxiliary queueing system are obtained, which lead to bounds on the stationary distribution of the queue lengths in the original queueing system. Using matrix-analytic methods, it is shown that the tail asymptotics of the stationary distribution is exact geometric, if the queue with the highest priority is overloaded.

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