A time varying filtering theory for constrained traffic regulation and dynamic service guarantees

By extending the filtering theory under the (min, +)-algebra to the time varying setting, we solve the problem of constrained traffic regulation and develop a calculus for dynamic service guarantees. For a constrained traffic regulation problem with maximum tolerable delay d and maximum buffer size q, the optimal regulator that generates the output traffic 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 bufferless device which optimally drops packets as necessary in order that its output be conformant to an envelope g. The maximal f-regulator is a buffered 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 filter 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, “filter 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