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

In this paper, we extend the ltering theory in 6] for deterministic traac regulation and service guarantees to the matrix setting. Such an extension enables us to model telecom-munication 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, \\lter bank summation" and performance bounds. As an application of the calculus, we derive service guarantees for networks with nested window ow control. In particular, service guarantees for networks with tandem ow control can be solved explicitly by the Gauss elimination.