Analyzing Weighted Round Robin policies with a stochastic comparison approach

We study queuing delays for Weighted Round Robin (WRR) scheduling policies. The delay characteristics of these policies can be estimated through worst-case bounds as other fair queuing scheduling policies. However, these deterministic bounds are in general not accurate and they require that the input process has been shaped. Under Markovian arrival hypothesis, the delay of WRR policies can be evaluated through Markovian numerical analysis. Nevertheless, this analysis is limited to small parameter sizes because of the state space explosion problem. We propose to apply the stochastic comparison approach. We build a bounding model based on the aggregation of sessions, and we show that under the same arrivals, the packet delays in the bounding model are larger in the st stochastic order sense than the packet delays in the original model. Due to this aggregation, the state space size is drastically reduced and we are able to provide stochastic delay bounds for WRR policies. We discuss the accuracy of the proposed bounds through numerical examples.