A Shift Varying Filtering Theory for Dynamic Service Guarantees

Abstract

We extend the recently developed filtering theory under (max,+)-algebra to shift varying setting and develop a calculus for dynamic service guarantees for variable length packet networks. By modifying the Chang’s traffic characterization to shift varying setting, we introduce two basic network elements for time varying input traffic models: (i) traffic regulators that generate G-regular marked point processes and (ii) dynamic G-server that provide service guarantees for marked point processes. Similar to shift invariant setting under (max,+)-algebra, network elements can be joined by concatenation, “filter bank summation,” and feedback to form a composite network element. We illustrate the use of framework by various examples like time varying G/G/1 queue, segmentation and reassembly, jitter control, damper and window flow control.