A number of studies have statistically characterized Internet flow traffic as a multifractal process. Knowing the average of, and probable fluctuations in, the amount of work arriving in a given system allows determination of the bandwidth needed to support quality of service requirements. The technical challenge, and the primary contribution of this paper, is the derivation of the queueing system fed by a multifractal envelope process, which provides an upper bound on the maximum queue length, and, in a subsequent calculation, the effective bandwidth.

The authors’ approach exploits the fact that a multifractal Brownian process can be locally modeled as a monofractal Brownian process, thereby transforming the problem of finding the solution to a stochastic system into the easier problem of finding a solution to a deterministic system. This simplification requires the Holder (Hurst) parameter, which indicates the scaling properties of the flow, to be continuously updated. In the end, however, this may turn out to be beneficial for real-time traffic streams using statistical multiplexing networks, as opposed to more common (and slower) circuit-switched networks.

The results demonstrate tight bounds for the solution when validated against either real or synthetically generated network traces; in contrast, the monofractal approach tends to overestimate bandwidth requirements. Finally, the authors extend the theory to a queue fed by several multifractal flows, and calculate the gain measure via the ratio of a system requiring n times the equivalent bandwidth of a flow to a system requiring the equivalent bandwidth for the aggregate of n homogeneous flows.