DIFFUSION APPROXIMATION FOR AN INPUT-QUEUED
SWITCH OPERATING UNDER A MAXIMUM WEIGHT
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.
proof builds on our own prior work on an invariance principle for
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,
For a copy, click here.
Last updated: February 20, 2013 >