Multifractal Modeling of Counting Processes of Long-range Dependent Network Traac

We study traac streams through their counting process representation. We examine the long-range-dependent (LRD) characteristics of such processes. We rst show that the measured LRD traac, as described by the interarrival time and packet size sequences , is suuciently well approximated by a synthesized stream formed by recording the counting state of the traac at the start of each time slot. We then model these counting processes by constructing a multiplicative multifractal process. The model only contains two parameters. One is used to indicate the mean of the counting process; the other is employed to describe the variation of the traac around the mean function. We show that this multifractal traac characterization has well de-ned burstiness descriptors, and is easy to construct. We consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by properly parameterized multifractal processes. In comparing the system-size tail distributions, we demonstrate our model to eeectively track the behavior exhibited by the system driven by the actual traac processes.