Modular Methodology for the Network Calculus in a Time-Varying Context

Network calculus (NC) is a set of rules and results for computing bounds for performance parameters of communication systems, such as end-to-end delay, maximum backlog, and service curves. Previous works show that the problem of determining performance bounds of communication networks is simplified if modeled using the dioid algebra. In this paper, we propose a methodology that allows the treatment of NC problems in a modular basis in a time-varying context, i.e., when curves vary with time. From the proposed methodology, we extend some results of the literature and derive new results on NC. Among the obtained results, we introduce an alternative representation of service guarantees that better explore the available knowledge of systems. We also define variable delay functions that lead to less conservative delay bounds than those in the literature. Finally, we analyze a FIFO multiplexer with M input flows.