Matrix extensions of the filtering theory for deterministic traffic regulation and service guarantees

Abstract

We extend the filtering theory, presented in a previous paper, for deterministic traffic regulation and service guarantees to the matrix setting. Such an extension enables us to model telecommunication networks as linear systems with multiple inputs and multiple outputs under the (min,+)-algebra. Analogous to the scalar setting, there is an associated calculus in the matrix setting, including feedback, concatenation, "filter bank summation", and performance bounds. As an application of the calculus, we derive service guarantees for networks with nested window flow control. In particular, service guarantees for networks with tandem flow control can be solved explicitly by the Gauss elimination.