Batch queues, reversibility and first-passage percolation

Batch queues, reversibility and first-passage percolation

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Article ID: iaor200971409
Country: Netherlands
Volume: 62
Issue: 4
Start Page Number: 411
End Page Number: 427
Publication Date: Aug 2009
Journal: Queueing Systems
Authors:
Keywords: batch queues, M/M/1 queues
Abstract:

We consider a model of queues in discrete time, with batch services and arrivals. The case where arrival and service batches both have Bernoulli distributions corresponds to a discrete-time M/M/1 queue, and the case where both have geometric distributions has also been previously studied. We describe a common extension to a more general class where the batches are the product of a Bernoulli and a geometric, and use reversibility arguments to prove versions of Burke's theorem for these models. Extensions to models with continuous time or continuous workload are also described. As an application, we show how these results can be combined with methods of Seppäläinen and O'Connell to provide exact solutions for a new class of first-passage percolation problems.

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