Stochastic Systems

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

Neil Stuart Walton

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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

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

First available in Project Euclid: 24 February 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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