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An asymptotically exact decomposition of coupled Brownian systems

Part of: Markov processes Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Kerry W. Fendick
Kerry W. Fendick*
Affiliation:
AT&T Bell Laboratories
*
∗ Postal address: AT&T Bell Laboratories, Room IF-401, 101 Crawfords Corner Road, Holmdel, NJ 07733–3030, USA.
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Abstract

Brownian flow systems, i.e. multidimensional Brownian motion with regulating barriers, can model queueing and inventory systems in which the behavior of different queues is correlated because of shared input processes. The behavior of such systems is typically difficult to describe exactly. We show how Brownian models of such systems, conditioned on one queue length exceeding a large value, decompose asymptotically into smaller subsystems. This conditioning induces a change in drift of the system's net input process and its components. The results here are analogous to results for jump-Markov queues recently obtained by Shwartz and Weiss. The Brownian setting leads to a simple description of the component processes' asymptotic behaviour, as well as to explicit distributional results.

Keywords

STOCHASTIC PROCESSESCONDITIONAL LIMIT THEOREMSREGULATED BROWNIAN MOTION

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 819 - 834
Copyright
Copyright © Applied Probability Trust 1993 

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