A Min-Plus System Theory for Constrained Tra c Regulation and Dynamic Service Guarantees

By extending the system theory under the (min;+)-algebra to the time varying setting, we solve the problem of constrained tra c regulation and develop a calculus for dynamic service guarantees. For a constrained tra c regulation problem with maximum tolerable delay d and maximum bu er size q, the optimal regulator that generates the output tra c conforming to a subadditive envelope f and minimizes the number of discarded packets is a concatenation of the g-clipper with g(t) = min[f(t+ d); f(t) + q] and the maximal f -regulator. The g-clipper is a bu erless device which optimally drops packets as necessary in order that its output be conformant to an envelope g. The maximal f -regulator is a bu ered device that delays packets as necessary in order that its output be conformant to an envelope f . The maximal 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.