On the Prediction of Average Queueing Delay with Self-Similar Traffic

Recent studies on a wide range of network traffic measurements including LAN and WAN have revealed the presence of self-similarity. These types of traffic hold statistical similarity across multiple time scales. Burstiness is retained even with the aggregating self-similar traffic. This property degrades the performance of a network. The queueing delay is one of the performance measures. In this study, a G/M/1 queueing model is used to model a network with self-similar traffic. The results of this study demonstrate that the delay exhibits a rise as degree of self-similarity increases. We compare an analytic average queueing delay of the self-similar traffic to the delay of simulated model to obtain a useful method for the delay prediction. By adjusting a single parameter of the truncated power-tail (TPT) distributions, we can make the analytic curve follow the simulation results. This allows us to predict the delay by computing the TPT once we measure the Hurst parameter of an input traffic and its arrival rate, and the utilization of a router. Our results can benefit control, design, and resource allocation of high-speed networks.