A Time Varying Filtering Theory for Constrained

By extending the ltering theory under the (min; +)-algebra to the time varying setting, we solve the problem of constrained traac regulation and develop a calculus for dynamic service guarantees. For a constrained traac regulation problem with maximum tolerable delay d and maximum buuer size q, the optimal regulator that generates the output traac conforming to a subadditive envelope f and minimizes the number of discarded packets is a concatenation of the g-clipper with g(t) = minf(t + d); f(t) + q] and the maximal f-regulator. The g-clipper is a buuerless device which optimally drops packets as necessary in order that its output be conformant to an envelope g. The maximal f-regulator is a buuered device that delays packets as necessary in order that its output be conformant to an envelope f. The f-regulator is a linear time invariant lter with impulse response f, under the (min; +)-algebra. To provide dynamic service guarantees in a network, we develop the concept of a dynamic server as a basic network element. Dynamic servers can be joined by concatenation, \\lter bank summation," and feedback to form a composite dynamic server. We also show that dynamic service guarantees for multiple input streams sharing a work conserving link can be achieved by a dynamic SCED (Service Curve Earliest Deadline) scheduling algorithm, if an appropriate admission control is enforced.