A filtering theory for deterministic traffic regulation

Abstract

We develop a filtering theory for deterministic traffic regulators that generate f-constrained outputs. We show that such regulators can be implemented by a linear time invariant filter with the impulse response f under the (min,+)-algebra if the function f is increasing and subadditive. The filtering approach not only yields easier proofs for more general results than those in the literature, but also allows us to design traffic regulators via systematic methods such as concatenation, filter bank summation, linear system realization, and FIR-IIR realization. The theory has many applications, including leaky buckets, traffic regulation for periodic constraint functions, and service curves. In particular, we find a new linear system realization and a new FIR-IIR realization for a concatenation of leaky buckets. Moreover, we find an FIR-IIR realization for traffic regulators with periodic constraint functions. We also show that such regulators, in conjunction with maximum delay guarantee, guarantee shifted-subadditive service curves. Based on this, we provide a couple of rules for service curve allocation among a concatenation of servers.