On temporal characteristics in an exponential queueing system with negative claims and a bunker for ousted claims

On temporal characteristics in an exponential queueing system with negative claims and a bunker for ousted claims

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Article ID: iaor2012186
Volume: 72
Issue: 12
Start Page Number: 2492
End Page Number: 2504
Publication Date: Dec 2011
Journal: Automation and Remote Control
Authors: ,
Keywords: multistage queues
Abstract:

We consider a queueing system with Poisson input streams of positive and negative claims, an infinite collector, and exponential service. A negative claim ousts a positive claim out of the collector queue and moves it to a bunker of unbounded capacity. If the collector is empty then a negative claim leaves the system with no influence on it. After a claim is serviced, the device receives the next claim from the collector or, if the collector is empty, from the bunker. For different combinations of FIFO and LIFO orders of choosing a claim for service from the collector’s queue, choosing a claim for service from the bunker’s queue, and ousting claims from the collector to the bunker, we obtain formulas for computing the stationary waiting time distribution for a claim to begin service and other temporal characteristics.

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