Residuated pairs in network analysis

Computer network can be analyzed linearly by idempotent system theory, residuation theory is one of main analyzing tools for idempotent mathematics. In this paper, we study the residuated function pairs that can be used in network modeling and analyzing, the basic properties of these pairs are obtained, and we also study their applications in network analysis. Our research shows that residuation theory is useful in computer network analysis especially in network calculus theory.