Duality of the Max-Plus and Min-Plus Network Calculus

Network calculus is a methodology for performance evaluation of communication networks that expresses the analysis of networks in a min-plus or max-plus algebra. In these algebras, the conventional addition and multiplication operations are replaced by the minimum or maximum operation, respectively, and addition. This monograph gives an accessible and concise review of the research conducted in Network Calculus to date. In doing so, it unearths the question: why are min-plus and max- plus calculus not isomorphic whereas the underlying min-plus and max-plus algebras upon which they are based are? This question is fully investigated and the differences between a max-plus and min-plus analysis are presented. This enables scheduling algorithms with rate and delay guarantees by service curves of the network calculus to be characterized, leading to useful results for their use in network research. The monograph is of interest to students and researchers working on the mathematical theory of networks.