Batch queues, reversibility and first-passage percolation

Details Batch queues, reversibility and first-passage percolation Batch queues, reversibility and first-passage percolation

2009-02-12

arxiv.org/abs/0902.2026v2

Mathematics

Probability

16 pages. Mostly minor revisions; some new explanatory text added in various places. Thanks to a referee for helpful comments

Scientific paper

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 Seppalainen and O'Connell to provide exact solutions for a new class of first-passage percolation problems.

Affiliated with

Also associated with

No associations

Rating

Batch queues, reversibility and first-passage percolation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Batch queues, reversibility and first-passage percolation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Batch queues, reversibility and first-passage percolation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-555856