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Analytical Performance Evaluation

The success of computer and communication systems strongly depends on their performance, typically reflected in the perception of speed. Optimizing system performance, subject to a set of resource and cost constraints, is thus a critical design goal for system engineers. An elegant technique to help in this matter is performance evaluation which can be performed either by measurements, simulation, or using theoretical methods. In particular, analytical performance evaluation has the fundamental merit of rapidly leading to rigorous and unequivocal insight into the behavior of systems which can be accordingly tuned and optimized.

Our own research is concerned with extending the theory of the stochastic network calculus, which is a probabilistic extension of the deterministic network calculus conceived by R. Cruz in the early 1990's. Over the past two decades the calculus has established itself as a versatile alternative methodology to the classical queueing theory for the performance analysis of computer and communication networks. Its prospect is that it can deal with problems that are fundamentally hard for queueing theory, based on the fact that it works with bounds rather than striving for exact solutions. We are in particular concerned with various fundamental research problems related to modelling and analyzing networks with flow transformations, or improving the bounds accuracy using refined inequalities. On the long term, we believe that our research can significantly contribute to establishing the stochastic network calculus as an indispensable mathematical tool for the performance analysis of resource sharing based systems.

Selected Publications

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
Organization ACM SIGMETRICS
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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