Long-Run Performance Analysis of a Multi-Scale TCP Traffic Model

The long-run queueing performance of a multi-scale TCP traffic model, the HOO model, is analysed. Since the model links the multi-scale behaviour with practical traffic elements and approximates TCP traffic very well, the analysis is expected to provide insights into the physical interpretation of multi-scale traffic and to give useful results for performance prediction. To derive a meaningful solution and avoid the extreme difficulty of an exact analysis, the authors adopt several techniques to track the problem, among which are techniques to establish equivalent processes to the traffic process or the queue content process in two cases, the case of fast flows and the case of slow flows. Quantitative results for the queue tails are obtained in both cases, and a unified form is derived. It indicates that three levels of traffic elements in different time scales, i.e. the connection, the burst and the packet, all affect the asymptotic queueing performance. It shows quantitatively how the connection determines the index of the queue tail, and the burst and the packet contribute to the tail with their averages. Used with simple statistical inferences, the analytical result is shown to predict the queueing performance of real traffic well.