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Of Kernels and Queues: when network calculus meets analytic combinatorics

Abstract : 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.
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Contributor : Céline Comte <>
Submitted on : Tuesday, October 9, 2018 - 9:10:54 AM
Last modification on : Friday, July 31, 2020 - 10:44:11 AM
Long-term archiving on: : Thursday, January 10, 2019 - 12:29:38 PM


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  • HAL Id : hal-01889101, version 1
  • ARXIV : 1810.04875



Anne Bouillard, Céline Comte, Élie de Panafieu, Fabien Mathieu. Of Kernels and Queues: when network calculus meets analytic combinatorics. NetCal 2018, Sep 2018, Vienne, Austria. ⟨hal-01889101⟩



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