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Kommunikation in Verteilten Systemen (KiVS) pp 181–192Cite as

Transformation-Based Network Calculus Applying Convex/Concave Conjugates

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Part of the book series: Informatik aktuell ((INFORMAT))

Abstract

Network calculus has successfully been applied to derive performance bounds for communication networks, whereas a number of issues still remain unsolved or are not well understood yet. Founded on min-plus convolution and de-convolution, network calculus obeys a strong analogy to system theory. However, system theory has been extended beyond the time domain, applying the Fourier transform and allowing for an efficient analysis in the frequency domain. A corresponding dual domain for network calculus has not been elaborated, so far. In this paper we show that in analogy to system theory such a dual domain for network calculus is given by convex/concave conjugates referred to also as Legendre transform. We provide solutions for dual operations and show that min-plus convolution and de-convolution become simple addition and subtraction in Legendre space.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik 4, RWTH Aachen, Ahornstr. 55, 52074, Aachen

    Markus Fidler

  2. IMST GmbH, Carl-Friedrich-Gauß-Str. 2, 47475, Kamp-Lintfort

    Stephan Recker

Authors
  1. Markus Fidler
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  2. Stephan Recker
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Editor information

Editors and Affiliations

  1. Fachbereich Informatik, Technische Universität Kaiserslautern, Postfach 3049, 67653, Kaiserslautern

    Paul Müller , Reinhard Gotzhein  & Jens B. Schmitt ,  & 

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© 2005 Springer-Verlag Berlin Heidelberg

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Fidler, M., Recker, S. (2005). Transformation-Based Network Calculus Applying Convex/Concave Conjugates. In: Müller, P., Gotzhein, R., Schmitt, J.B. (eds) Kommunikation in Verteilten Systemen (KiVS). Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27301-8_15

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