Slope Domain Modeling and Analysis of Data Communication Networks: A Network Calculus Complement

Min-plus filtering theory (or its dual, max-plus), commonly called Network Calculus (NC), is a sophisticated modern framework for modeling and analysis of data communication networks. In this paper, we complement NC theory by proposing the novel application of slope domain analysis in NC using the slope transform, an analytical framework which is analogous to frequency domain analysis based on the Fourier transform in traditional system theory. We describe the principles and properties of slope domain analysis, and how it can be effectively applied in analysis of computer networks. We illustrate the application of the proposed method in system identification and priority scheduling to demonstrate that slope domain analysis is a much more convenient and efficient, and in some cases, the only viable approach to solving some NC problems. We conclude the paper by presenting the Legendre and Fenchel transforms as special cases of the slope transform that facilitate fast calculations.