On Deterministic Tra c Regulation and Service Guarantees: A Systematic Approach by Filtering

In this paper, we develop a ltering theory for deterministic traac regulation and service guarantees under the (min; +)-algebra. We show that traac regulators that generate f-upper constrained outputs can be implemented optimally by a linear time invariant lter with the impulse response f under the (min; +)-algebra, where f is the subadditive closure deened in the paper. Analogous to the classical ltering theory, there is an associate calculus, including feedback, concatenation, \\lter bank summation" and performance bounds. The calculus is also applicable to the recently developed concept of service curves that can be used for deriving deterministic service guarantees. Our ltering approach not only yields easier proofs for more general results than those in the literature, but also allows us to design traac regulators via systematic methods such as concatenation, lter bank summation, linear system realization, and FIR-IIR realization. We illustrate the use of the theory by considering a window ow control problem and a service curve allocation problem.