Stochastic Systems

Flow-level convergence and insensitivity for multi-class queueing networks

Neil Stuart Walton

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Abstract

We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochastic model as a model of document transfer in a communication network where the documents transferred have a general distribution. We prove the weak convergence of the multi-class queueing process to the document transfer process. Our convergence result allows the comparison of general document size distributions, and consequently, we prove general insensitivity results for the limit queueing process. We discuss how this separation of time-scales method of proving insensitivity may be applied to other insensitive queueing systems.

Article information

Source
Stoch. Syst., Volume 2, Number 1 (2012), 115-148.

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1393252042

Digital Object Identifier
doi:10.1214/11-SSY025

Mathematical Reviews number (MathSciNet)
MR3352976

Zentralblatt MATH identifier
1298.60094

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60G17: Sample path properties
Secondary: 90B18: Communication networks [See also 68M10, 94A05]

Citation

Walton, Neil Stuart. Flow-level convergence and insensitivity for multi-class queueing networks. Stoch. Syst. 2 (2012), no. 1, 115--148. doi:10.1214/11-SSY025. https://projecteuclid.org/euclid.ssy/1393252042


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