DMTCS Proceedings, Discrete Random Walks, DRW'03

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DMTCS Conference vol AC (2003), pp. 69-82


Discrete Random Walks, DRW'03

Cyril Banderier and Christian Krattenthaler (eds.)

DMTCS Conference Volume AC (2003), pp. 69-82

author: Moez Draief, Jean Mairesse and Neil O'Connell
title: Joint Burke's Theorem and RSK Representation for a Queue and a Store
keywords: Single server queue, storage model, Burke's theorem, non-colliding random walks, tandem of queues, Robinson-Schensted-Knuth algorithm
abstract: Consider the single server queue with an infinite buffer and a FIFO discipline, either of type
or Geom/Geom/1. Denote by
the arrival process and by
the services. Assume the stability condition to be satisfied. Denote by
the departure process in equilibrium and by
the time spent by the customers at the very back of the queue. We prove that
has the same law as
which is an extension of the classical Burke Theorem. In fact,
can be viewed as the departures from a dual
model. This duality between the two models also appears when studying the transient behavior of a tandem by means of the RSK algorithm: the first and last row of the resulting semi-standard Young tableau are respectively the last instant of departure in the queue and the total number of departures in the store.
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reference: Moez Draief and Jean Mairesse and Neil O'Connell (2003), Joint Burke's Theorem and RSK Representation for a Queue and a Store, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 69-82
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