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Diffusion approximation for an input-queued switch operating under a maximum weight matching policy

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Author(s): Weining Kang | Ruth J. Williams,

Journal: Stochastic Systems
ISSN 1946-5238

Volume: 2;
Issue: 2;
Start page: 277;
Date: 2012;
Original page

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

ABSTRACT
For 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].
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