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Exponential Supermartingales for Evaluating End-to-End Backlog Bounds
Citation key C-ESEEEBB-07
Author Ciucu, Florin
Pages 21–23
Year 2007
ISSN 0163-5999
DOI http://dx.doi.org/10.1145/1330555.1330565
Address New York, NY, USA
Journal Performance Evaluation Review
Volume 35
Number 2
Note appeared also at the Ninth Workshop on Mathematical Performance Modeling and Analysis (MAMA 2007), held in conjunction with ACM Sigmetrics 2007
Publisher ACM
Abstract A common problem arising in network performance analysis with the stochastic network calculus is the evaluation of (min, +) convolutions. This paper presents a method to solve this problem by applying a maximal inequality to a suitable constructed supermartingale. For a network with D/M input, end-to-end backlog bounds obtained with this method improve existing results at low utilizations. For the same network, it is shown that at utilizations smaller than a certain threshold, fluid-flow models may lead to inaccurate approximations of packetized models.
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