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November, 1995 Diffusion Approximation for Open State-Dependent Queueing Networks in the Heavy Traffic Situation
Keigo Yamada
Ann. Appl. Probab. 5(4): 958-982 (November, 1995). DOI: 10.1214/aoap/1177004602

Abstract

We consider open queueing networks in which arrival and service rates are dependent on the state (i.e., queue length) of the network. They are modeled as multidimensional birth and death processes. If a heavy traffic condition is sastisfied on the behavior of arrival and service rates when the queue length becomes very large, it is shown that a properly normalized sequence of queue length converges in law to a reflecting diffusion process.

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Keigo Yamada. "Diffusion Approximation for Open State-Dependent Queueing Networks in the Heavy Traffic Situation." Ann. Appl. Probab. 5 (4) 958 - 982, November, 1995. https://doi.org/10.1214/aoap/1177004602

Information

Published: November, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0870.60025
MathSciNet: MR1384362
Digital Object Identifier: 10.1214/aoap/1177004602

Subjects:
Primary: 60F17
Secondary: 60H30 , 60K25

Keywords: diffusion approximation , heavy traffic condition , multidimensional diffusion with oblique reflection , Queueing network

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 4 • November, 1995
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