Open AccessOpen Access licenseAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Go to SectionOpen AccessOpen Access license HomeStochastic SystemsVol. 2, No. 2 Diffusion Approximation for an Input-queued Switch Operating under a Maximum Weight Matching PolicyW. N. Kang, R. J. WilliamsW. N. Kang, R. J. WilliamsPublished Online:19 Dec 2012https://doi.org/10.1287/12-SSY061AbstractFor N ≥ 2, we consider an N × N input-queued switch operating under a maximum weight matching policy. We establish a diffusion approximation for a (2N − 1)-dimensional workload process associated with this switch when all input ports and output ports are heavily loaded. The diffusion process is a semimartingale reflecting Brownian motion living in a polyhedral cone with N2 boundary faces, each of which has an associated constant direction of reflection. Our proof builds on our own prior work [13] on an invariance principle for semimartingale reflecting Brownian motions in piecewise smooth domains and on a multiplicative state space collapse result for switched networks established by Shah and Wischik in [19]. Previous Back to Top Next FiguresReferencesRelatedInformationCited ByHeavy-Traffic Analysis of Queueing Systems with No Complete Resource PoolingDaniela Andrea Hurtado Lange, Siva Theja Maguluri2 March 2022 | Mathematics of Operations Research, Vol. 0, No. 0Fluctuation Bounds for the Max-Weight Policy with Applications to State Space CollapseArsalan Sharifnassab, John N. Tsitsiklis, S. Jamaloddin Golestani9 April 2020 | Stochastic Systems, Vol. 10, No. 3Collaboration and Multitasking in Networks: Prioritization and Achievable CapacityItai Gurvich, Jan A. Van Mieghem19 May 2017 | Management Science, Vol. 64, No. 5 Volume 2, Issue 2December 2012Pages 232-446 Article Information Metrics Downloaded 48 times in the past 12 months Information Received:January 01, 2012Published Online:December 19, 2012 Copyright © 2012, The author(s)Cite asW. N. Kang, R. J. Williams (2012) Diffusion Approximation for an Input-queued Switch Operating under a Maximum Weight Matching Policy. Stochastic Systems 2(2):277-321. https://doi.org/10.1287/12-SSY061 KeywordsInput-queued switchmaximum weight matching policydiffusion approximationheavy trafficsemimartingale reflecting Brownian motion (SRBM)PDF download