DIFFUSION APPROXIMATION FOR AN INPUT-QUEUED SWITCH OPERATING UNDER A MAXIMUM WEIGHT MATCHING POLICY
W. N. Kang and R. J. Williams
For N>1, we consider an NxN 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 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.

This paper is published in Stochastic Systems, 2 (2012), 277-321, DOI: 10.1214/12-SSY061. For a copy, click here.

Last updated: February 20, 2013