A Time Varying Network Calculus

Network calculus is widely used in network analysis and quality of service research, but till now the main work of the network calculus theory focuses on the time invariant field, and little work on the case that arrival curve and service curve are time varying functions. We propose a time varying network calculus theory, define the concept of time varying arrival curve and time varying service curve, obtain the time varying expression of delay bound, backlog bound and output burst. We also propose a method which use the closure operation to get the expression of a time invariant function, and use this method to analyze traffic clipper. The method proved its efficiency and simplicity. We also analyze the greedy shaper with non-empty initial buffer, and find that in this scenario, using time varying calculus is more simple.