Discrete Random Walks, DRW'03
Cyril Banderier and Christian Krattenthaler (eds.)
DMTCS Conference Volume AC (2003), pp. 6982
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, noncolliding random walks, tandem of queues, RobinsonSchenstedKnuth algorithm 
abstract: 
Consider the single server queue with an infinite buffer
and a FIFO discipline, either of type
M/M/1
or Geom/Geom/1. Denote by
A
the arrival process and by
s
the services. Assume the stability condition to be
satisfied. Denote by
D
the departure process in equilibrium and by
r
the time spent by the customers at the very back of
the queue. We prove that
(D,r)
has the same law as
(A,s)
which is an extension of the classical Burke Theorem.
In fact,
r
can be viewed as the departures from a dual
storage
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 semistandard 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. 6982 
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