Stochastic bounds on delays of fair queueing algorithms

We study the delay characteristics of fair queueing algorithms with a stochastic comparison approach. In integrated services networks, fair queueing (FQ) policies have received much attention, because they can guarantee an end-to-end session delay bound when the burstiness of the session traffic is bounded, and they ensure the fair allocation of the bandwidth. A large class of FQ policies attempt to emulate generalized processor sharing (GPS) policy by assigning timestamps to cells. These GPS related policies have quite complex dynamic, and their exact analytical analysis is not tractable. The delay characteristics of these algorithms are evaluated by considering the worst-case, when sources have a bounded burstiness. In fact, these are deterministic delay bounds which do not always provide an insight on the underlying policies. For instance, in the case of leaky bucket constrained traffic, these bounds correspond to the case when all sessions are greedy (each session must empty the token pool in the minimum time after becoming active). We propose a methodology to analyze delay characteristics of a class of GPS-related FQ policies with general source models by providing stochastic bounds on their delay distribution. These stochastic bounds are obtained by analyzing two modified weighted round robin (WRR) policies. Clearly, since cells are scheduled periodically according to a predefined list under WRR-related policies, their models are simpler than the models of GPS-related policies.