Some Principles of Network Calculus Revisited

Network calculus is a mathematical theory dealing with queueing problems in packet-switched computer networks. It provides algorithms to determine resource requirements of traffic flows using arrival and service curves and describes delays and backlogs in network systems. Network calculus framework is based on a min-plus algebra which allows to transform complex network optimization problems into analytically tractable ones. Recently, a fundamental book on principles, tools, techniques, and applications of network calculus, entitled: Network Calculus. A Theory of Deterministic Queuing Systems for the Internet, has been published by J. Y. Le Boudec and P. Thiran. Here, we refer to it in our refinements of proof of one important theorem and its extension. The objective of this paper is twofold. First, we complete one of basic results regarding a network element that is called in network calculus a greedy shaper. Second, we present also the results of some illustrative calculations and measurements of network service curve. They aim in better understanding of its properties.