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Diffusion Approximation of State-Dependent G-Networks Under Heavy Traffic

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Saul C. Leite  and
Marcelo D. Fragoso
Saul C. Leite*
Affiliation:
LNCC
Marcelo D. Fragoso*
Affiliation:
LNCC
*
∗Postal address: Departamento de Sistemas e Controle, LNCC, CEP 25651-075, Quitandinha, Petrópolis, RJ, Brazil.
∗∗Email address: Email address: [email protected]
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Abstract

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This paper is concerned with the characterization of weak-sense limits of state-dependent G-networks under heavy traffic. It is shown that, for a certain class of networks (which includes a two-layer feedforward network and two queues in tandem), it is possible to approximate the number of customers in the queue by a reflected stochastic differential equation. The benefits of such an approach are that it describes the transient evolution of these queues and allows the introduction of controls, inter alia. We illustrate the application of the results with numerical experiments.

Keywords

Heavy-traffic approximationG-network

MSC classification

Secondary: 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 347 - 362
Copyright
Copyright © Applied Probability Trust 2008 

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