Stochastic delay bounds of fair queuing policies by analyzing weighted round robin-related policies

We propose to apply the stochastic comparison method to evaluate the delay characteristics of generalized processor sharing (GPS)-related fair queuing (FQ) policies in a stochastic setting. These policies have complex dynamics, and their delays are evaluated through deterministic worst-case bounds under the leaky bucket-constrained traffics. Our approach consists to define “bounding” weighted round robin (WRR)-related policies for some GPS-related policies: under the same arrival process, the departure instants under the bounding policy are later or equal to the departure instants under the FQ policy for each cell. This sample-path comparison allows us to establish the stochastic comparison of delay distributions in the strong stochastic ordering sense. By defining WRR-related policies as bounding policies, we are able to carry out the Markovian analysis. Since our approach lets us to take into account explicitly the arrival process, the proposed bounds give more insight on delay characteristics than the deterministic bounds.