Stochastic Systems

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

W. N. Kang and R. J. Williams

Full-text: Open access

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].

Article information

Source
Stoch. Syst., Volume 2, Number 2 (2012), 277-321.

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1393252025

Digital Object Identifier
doi:10.1214/12-SSY061

Mathematical Reviews number (MathSciNet)
MR3354769

Zentralblatt MATH identifier
1296.60212

Subjects
Primary: 60J60: Diffusion processes [See also 58J65] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 90B36: Scheduling theory, stochastic [See also 68M20]

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

Citation

Kang, W. N.; Williams, R. J. Diffusion approximation for an input-queued switch operating under a maximum weight matching policy. Stoch. Syst. 2 (2012), no. 2, 277--321. doi:10.1214/12-SSY061. https://projecteuclid.org/euclid.ssy/1393252025


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References

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