Network Calculus and Conjugate Duality in Network Performance Analysis

Network calculus has successfully been deployed to derive deterministic performance bounds in packet-switching networks. Recently, the deployment of the conjugate convex or concave transforms has been proposed as dual approach to this calculus. The attractiveness of this conjugate network calculus is based on the fact that the Min-Plus convolution and deconvolution become the more convenient operators addition and subtraction in the conjugate transform domain. However, the derivation of performance bounds in this domain has not been elaborated so far. In this work we deploy the theory of conjugate duality in optimization problems in order to derive closed form expressions for the maximum backlog and delay in the conjugate transform domain. We illustrate the application of conjugate network calculus while also pointing on the deficiencies compared to calculus in the time domain.