Skip to Main content Skip to Navigation
Conference papers

Joint Burke's Theorem and RSK Representation for a Queue and a Store

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 $\mathcal{A}$ the arrival process and by $s$ the services. Assume the stability condition to be satisfied. Denote by $\mathcal{D}$ the departure process in equilibrium and by $r$ the time spent by the customers at the very back of the queue. We prove that $(\mathcal{D},r)$ has the same law as $(\mathcal{A},s)$ 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 semi-standard Young tableau are respectively the last instant of departure in the queue and the total number of departures in the store.
Complete list of metadata

Cited literature [24 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Wednesday, August 12, 2015 - 9:07:45 AM
Last modification on : Friday, November 19, 2021 - 6:06:03 PM
Long-term archiving on: : Friday, November 13, 2015 - 11:37:56 AM


Publisher files allowed on an open archive




Moez Draief, Jean Mairesse, Neil O'Connell. Joint Burke's Theorem and RSK Representation for a Queue and a Store. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.69-82, ⟨10.46298/dmtcs.3339⟩. ⟨hal-01183934⟩



Record views


Files downloads