Of Kernels and Queues: when network calculus meets analytic combinatorics

Stochastic network calculus is a tool for computing error bounds on the performance of queueing systems. However, deriving accurate bounds for networks consisting of several queues or subject to non-independent traffic inputs is challenging. In this paper, we investigate the relevance of the tools f...

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Bibliographic Details
Published inarXiv.org
Main Authors Bouillard, Anne, Comte, Céline, Élie De Panafieu, Mathieu, Fabien
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.10.2018
Subjects
Combinatorial analysis
Combinatorics
Kernels
Mathematical analysis
Queues
Queuing theory
Software
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ISSN2331-8422

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Summary:Stochastic network calculus is a tool for computing error bounds on the performance of queueing systems. However, deriving accurate bounds for networks consisting of several queues or subject to non-independent traffic inputs is challenging. In this paper, we investigate the relevance of the tools from analytic combinatorics, especially the kernel method, to tackle this problem. Applying the kernel method allows us to compute the generating functions of the queue state distributions in the stationary regime of the network. As a consequence, error bounds with an arbitrary precision can be computed. In this preliminary work, we focus on simple examples which are representative of the difficulties that the kernel method allows us to overcome.
Bibliography:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422