Markovian bulk-arrival and bulk-service queues with state-dependent control

Markovian bulk-arrival and bulk-service queues with state-dependent control

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Article ID: iaor20101632
Volume: 64
Issue: 3
Start Page Number: 267
End Page Number: 304
Publication Date: Mar 2010
Journal: Queueing Systems
Authors: , , ,
Keywords: bulk queues
Abstract:

We study a modified Markovian bulk-arrival and bulk-service queue incorporating state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated and the relationship with our queueing model is examined and exploited. Equilibrium behaviour is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting time and busy period distributions are answered in detail and the Laplace transforms of these distributions are presented. Further properties including expectations of hitting times and busy period are also explored.

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