Constrained Traffic Regulation and Dynamic Service Guarantees

Abstract

By extending the filtering theory under the (min, +)-algebra to the time varying setting, in this chapter we will 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 an f-upper constrained output and minimizes the number of discarded packets is a concatenation of the maximal g-clipper with g(t) = min[f(t+d),f(t)+q] and the maximal f-regulator. The maximal g-clipper is a bufferless device which optimally drops packets as necessary in order that its output is g-upper constrained. The maximal f-regulator is a buffered device that delays packets as necessary in order that its output is f-upper constrained. As discussed before, the maximal f-regulator with the input A and the output B can be implemented by

$$ B\left( t \right) = \mathop {\min }\limits_{0 \leqslant s \leqslant t} \left[ {A\left( s \right) + f\left( {t - s} \right)} \right]. $$