Abstract
Network calculus has successfully been applied to derive service guarantees for per-flow Integrated Services networks. Recent extensions also allow providing performance bounds for aggregate-based Differentiated Services domains, but with a significant increase in complexity. Further on, a number of issues still remain unsolved or are not well understood yet.
Founded on 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 the 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. Finally we address an aggregate scheduling example, where the Legendre transform allows deriving a new, explicit, and clear solution.
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Fidler, M., Recker, S. (2005). A Dual Approach to Network Calculus Applying the Legendre Transform. In: Ajmone Marsan, M., Bianchi, G., Listanti, M., Meo, M. (eds) Quality of Service in Multiservice IP Networks. QoS-IP 2004. Lecture Notes in Computer Science, vol 3375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30573-6_3
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DOI: https://doi.org/10.1007/978-3-540-30573-6_3
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