## DMTCS Proceedings, Discrete Random Walks, DRW'03

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

## Discrete Random Walks, DRW'03

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

author: Moez Draief, Jean Mairesse and Neil O'Connell Joint Burke's Theorem and RSK Representation for a Queue and a Store Single server queue, storage model, Burke's theorem, non-colliding random walks, tandem of queues, Robinson-Schensted-Knuth algorithm 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 semi-standard Young tableau are respectively the last instant of departure in the queue and the total number of departures in the store. If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. 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 For a corresponding BibTeX entry, please consider our BibTeX-file. dmAC0107.ps.gz (64 K) dmAC0107.ps (188 K) dmAC0107.pdf (160 K)

Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.

Automatically produced on Di Sep 27 10:09:16 CEST 2005 by gustedt