%0 Journal Article
%T Diffusion approximation for an input-queued switch operating under a maximum weight matching policy
%A Weining Kang
%A Ruth J. Williams
%J Stochastic Systems
%D 2012
%I Institute for Operations Research and the Management Sciences (INFORMS), Applied Probability Society
%X For N ¡Ý 2, we consider an N ¡Á 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].
%K Input-queued switch
%K maximum weight matching policy
%K diffusion approximation
%K heavy traffic
%K semimartingale reflecting Brownian motion (SRBM)
%U http://www.i-journals.org/ssy/viewarticle.php?id=61&layout=abstract