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2012 Diffusion approximation for an input-queued switch operating under a maximum weight matching policy
W. N. Kang, R. J. Williams
Stoch. Syst. 2(2): 277-321 (2012). DOI: 10.1214/12-SSY061

Abstract

For $N\geq 2$, we consider an $N\times N$ 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 $N^{2}$ 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].

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W. N. Kang. R. J. Williams. "Diffusion approximation for an input-queued switch operating under a maximum weight matching policy." Stoch. Syst. 2 (2) 277 - 321, 2012. https://doi.org/10.1214/12-SSY061

Information

Published: 2012
First available in Project Euclid: 24 February 2014

zbMATH: 1296.60212
MathSciNet: MR3354769
Digital Object Identifier: 10.1214/12-SSY061

Subjects:
Primary: 60J60 , 60J70 , 60K30 , 90B36

Keywords: diffusion approximation , heavy traffic , Input-queued switch , maximum weight matching policy , semimartingale reflecting Brownian motion (SRBM)

Rights: Copyright © 2012 INFORMS Applied Probability Society

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