Queues, stores, and tableaux
Draief, Moez, Mairesse, Jean and O'Connell, Neil. (2005) Queues, stores, and tableaux. Journal of Applied Probability, Vol.42 (No.4). pp. 1145-1167. ISSN 0021-9002Full text not available from this repository.
Consider the single-server queue with an infinite buffer and a first-in-first-out 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 sequence of departures from a dual storage model. This duality between the two models also appears when studying the transient behaviour of a tandem by means of the Robinson-Schensted-Knuth algorithm: the first and last rows of the resulting semistandard Young tableau are respectively the last instant of departure from the queue and the total number of departures from the store.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Journal of Applied Probability|
|Publisher:||Applied Probability Trust|
|Official Date:||December 2005|
|Number of Pages:||23|
|Page Range:||pp. 1145-1167|
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