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dc.contributor.authorGamarnik, David
dc.contributor.authorRikun, Alexander Anatolyevich
dc.contributor.authorBertsimas, Dimitris J
dc.date.accessioned2011-06-17T15:40:21Z
dc.date.available2011-06-17T15:40:21Z
dc.date.issued2011-03
dc.date.submitted2009-11
dc.identifier.issn1526-5463
dc.identifier.issn0030-364X
dc.identifier.urihttp://hdl.handle.net/1721.1/64477
dc.description.abstractPerformance analysis of queueing networks is one of the most challenging areas of queueing theory. Barring very specialized models such as product-form type queueing networks, there exist very few results that provide provable nonasymptotic upper and lower bounds on key performance measures. In this paper we propose a new performance analysis method, which is based on the robust optimization. The basic premise of our approach is as follows: rather than assuming that the stochastic primitives of a queueing model satisfy certain probability laws—such as i.i.d. interarrival and service times distributions—we assume that the underlying primitives are deterministic and satisfy the implications of such probability laws. These implications take the form of simple linear constraints, namely, those motivated by the law of the iterated logarithm (LIL). Using this approach we are able to obtain performance bounds on some key performance measures. Furthermore, these performance bounds imply similar bounds in the underlying stochastic queueing models. We demonstrate our approach on two types of queueing networks: (a) tandem single-class queueing network and (b) multiclass single-server queueing network. In both cases, using the proposed robust optimization approach, we are able to obtain explicit upper bounds on some steady-state performance measures. For example, for the case of TSC system we obtain a bound of the form C(1 – {rho})–1 ln ln((1 – {rho})–1) [C(1-p) superscript -1 ln ln ((1 - p) superscript -1)]on the expected steady-state sojourn time, where C is an explicit constant and {rho} is the bottleneck traffic intensity. This qualitatively agrees with the correct heavy traffic scaling of this performance measure up to the ln ln((1 – {rho})–1) [ln ln((1 - p) superscript -1)] correction factor.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant DMI-0556106)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant CMMI-0726733)en_US
dc.language.isoen_US
dc.publisherINFORMS / Operations Research Society of Americaen_US
dc.relation.isversionofhttp://dx.doi.org/10.1287/opre.1100.0879en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceMIT web domainen_US
dc.titlePerformance analysis of queueing networks via robust optimizationen_US
dc.typeArticleen_US
dc.identifier.citationBertsimas, Dimitris, David Gamarnik, and Alexander Anatoliy Rikun. “Performance Analysis of Queueing Networks via Robust Optimization.” OPERATIONS RESEARCH 59.2 (2011) : 455-466. Copyright © 2011 by INFORMS.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Operations Research Centeren_US
dc.contributor.departmentSloan School of Managementen_US
dc.contributor.approverBertsimas, Dimitris J.
dc.contributor.mitauthorBertsimas, Dimitris J.
dc.contributor.mitauthorGamarnik, David
dc.contributor.mitauthorRikun, Alexander Anatolyevich
dc.relation.journalOperations Researchen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsBertsimas, D.; Gamarnik, D.; Rikun, A. A.en
dc.identifier.orcidhttps://orcid.org/0000-0002-1985-1003
dc.identifier.orcidhttps://orcid.org/0000-0001-8898-8778
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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