Positive Harris recurrence and diffusion scale analysis of a push pull queueing network

Nazarathy, Yoni and Weiss, Gideon (2010) Positive Harris recurrence and diffusion scale analysis of a push pull queueing network. Performance Evaluation, 67 4: 201-217. doi:10.1016/j.peva.2009.09.010

Author Nazarathy, Yoni
Weiss, Gideon
Title Positive Harris recurrence and diffusion scale analysis of a push pull queueing network
Journal name Performance Evaluation   Check publisher's open access policy
ISSN 0166-5316
Publication date 2010-04-01
Sub-type Article (original research)
DOI 10.1016/j.peva.2009.09.010
Volume 67
Issue 4
Start page 201
End page 217
Total pages 17
Editor Tijani Chahed
Luciano Lenzini
Nahum Shimkin
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Abstract We consider a push pull queueing network with two servers and two types of job which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is similar to the Kumar–Seidman Rybko–Stolyar (KSRS) multi-class queueing network, with the distinction that instead of random arrivals, there is an infinite supply of jobs of both types. Unlike the KSRS network, we can find policies under which our push pull network works at full utilization, with both servers busy at all times, and without being congested. We perform fluid and diffusion scale analysis of this network under such policies, to show fluid stability, positive Harris recurrence, and to obtain a diffusion limit for the network. On the diffusion scale the network is empty, and the departures of the two types of job are highly negatively correlated Brownian motions. Using similar methods we also derive a diffusion limit of a re-entrant line with an infinite supply of work.
Keyword Queueing networks
Push pull
Infinite virtual queues
Fluid models
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Special issue: Performance Evaluation Methodologies and Tools: Selected Papers from VALUETOOLS 2008

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
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Created: Fri, 27 Apr 2012, 22:57:02 EST by Kay Mackie on behalf of Mathematics