Filtering Theory for Deterministic Traffic Regulation and Service Guarantees

Abstract

In this chapter, we introduce the filtering theory for deterministic traffic regulation and service guarantees in [36,72,5,135]. The filtering theory is developed under the (min, +)-algebra, where one replaces the usual addition by the min operator and the usual multiplication by the addition operator. As in the classical linear system theory, the filtering theory treats an arrival process A (or a departure process B) as a signal and a network as a system.A signal f≡{f(t),t=0,1,2…}is a nonnegative and increasing function. A signal is said to be larger than another if all its values at any time t are larger. Two basic operations for signals under the (min, +)-algebra are considered, the "addition" operation ® and the "multiplication" operation *.