Geodesic
Joint Burke's Theorem and RSK Representation for a Queue and a Store
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003).

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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. 
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     author = {Draief, Moez and Mairesse, Jean and O'Connell, Neil},
     title = {Joint {Burke's} {Theorem} and {RSK} {Representation} for a {Queue} and a {Store}},
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Draief, Moez; Mairesse, Jean; O'Connell, Neil. Joint Burke's Theorem and RSK Representation for a Queue and a Store. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03), DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) (2003). doi : 10.46298/dmtcs.3339. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3339/

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