Multifractal modeling of counting processes of long-range dependent network traffic

Source traffic streams as well as aggregated traffic flows often exhibit long-range-dependent (LRD) properties. In this paper, we study traffic streams through their counting process representation. We first study the condition for the measured LRD traffic, as described by the interarrival time and packet size sequences, to be sufficiently well approximated by a synthesized stream formed by recording the counting state of the traffic at the start of each time slot. We then demonstrate that the burstiness of the counting processes is not well characterized by the Hurst parameter. We model a counting process by constructing a multiplicative multifractal process, which contains only one or two parameters. We study the LRD property of such processes, and show that the model has well-defined burstiness descriptors, and are 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 effectively track the behavior exhibited by the system driven by the actual traffic processes. Our study may help resolve a hot debate on the modeling of an often used trace of VBR video traffic.