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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

Non-asymptotic Delay Bounds for Networks with Heavy-Tailed Traffic
Citation key LBC-NDBNHTT-10
Author Liebeherr, Jörg and Burchard, Almut and Ciucu, Florin
Title of Book Proceedings of IEEE INFOCOM '10
Pages 1–9
Year 2010
ISBN 978-1-4244-5836-3
ISSN 0743-166X
DOI http://dx.doi.org/10.1109/INFCOM.2010.5461913
Location San Diego, CA, USA
Month March
Publisher IEEE
Abstract Traffic with self-similar and heavy-tailed characteristics has been widely reported in networks, yet, only few analytical results are available for predicting the delay performance of such networks. We address a particularly difficult type of heavy-tailed traffic where only the first moment can be computed, and present the first non-asymptotic end-to-end delay bounds for such traffic. The derived performance bounds are non-asymptotic in that they do not assume a steady state, large buffer, or many sources regime. Our analysis considers a multi-hop path of fixed-capacity links with heavy-tailed self-similar cross traffic at each node. A key contribution of the analysis is a probabilistic sample-path bound for heavy-tailed arrival and service processes, which is based on a scale-free sampling method. We explore how delays scale as a function of the length of the path, and compare them with lower bounds. A comparison with simulations illustrates pitfalls when simulating self-similar heavy-tailed traffic, providing further evidence for the need of analytical bounds.
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