The Annals of Applied Probability

Diffusion Approximation for Open State-Dependent Queueing Networks in the Heavy Traffic Situation

Keigo Yamada

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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.

Article information

Source
Ann. Appl. Probab. Volume 5, Number 4 (1995), 958-982.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1177004602

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aoap/1177004602

Mathematical Reviews number (MathSciNet)
MR1384362

Zentralblatt MATH identifier
0870.60025

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Diffusion approximation queueing network heavy traffic condition multidimensional diffusion with oblique reflection

Citation

Yamada, Keigo. Diffusion Approximation for Open State-Dependent Queueing Networks in the Heavy Traffic Situation. The Annals of Applied Probability 5 (1995), no. 4, 958--982. doi:10.1214/aoap/1177004602. http://projecteuclid.org/euclid.aoap/1177004602.


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