The Concept of Relevant Time Scales and Its Application to Queuing Analysis of Self-Similar Traffic (or Is Hurst Naughty or Nice?)

Recent traffic analyses from various packet networks have shown the existence of long-range dependence in bursty traffic. In evaluating its impact on queuing performance, earlier investigations have noted how the presence of long-range dependence, or a high value of the Hurst parameter H, is often associated with surprisingly large queue sizes. As a result, a common impression has been created of expecting queuing performance to be worse as H increases, but this impression can be misleading. In fact, there are examples in which larger values of H are associated with smaller queues. So the question is how can one tell whether queuing performance would improve or degrade as H rises? In this paper, we show that the relative queuing performance can be assessed by identifying a couple of time scales. First, in comparing a high-H process with a low-H process, there is a unique time scale tm at which the variances of the two processes match (assuming exact, second-order self similarity for bo..