Network Traffic Models:
Correlational and Distributional Effects

The foundational work of Leland, Taqqu, Willinger, and Wilson demonstrated the presence of long-range dependence in LAN traffic. A large body of research followed, firmly establishing that the Poisson process is a poor model of the packet arrival process in both LAN and Wide-Area network traffic. Poisson processes not only lack long-range dependence, but also the variance of the number of arrivals per unit time is necessarily equal to the mean. Several studies have demonstrated that, in real network traffic, the variance is commonly much larger than the
mean.

These findings preclude the extensive use of analytic modeling in the design of network components such as routers and switches. To accurately predict the behavior of components under realistic workloads designers have turned to simulation, and there is now a considerable interest in the construction of synthetic workloads to drive the simulations.

An ideal synthetic workload reflects both the distributional and correlational aspects of its real counterpart, but constructing such workloads has proven quite challenging. Random sampling from an empirical distribution (as is done in tcplib) captures distributional effects at the expense of correlational ones. Fractional Gaussian noise models capture correlational effects but match only two moments of the target distribution.

In this work we seek to evaluate the impact of distributional and correlation factors in the arrival stream on the predicted performance of network components and to identify improved methods for artificial traffic synthesis. The results of the first phase of the investigation were published in the Proceedings of CMG '99. That paper describes a new method for synthesizing fractional Gaussian noise and demonstrates that the fGn-synthesized counterparts of real workloads can significantly underestimate queuing delays and packet loss. That paper is available here in .pdf format. The presentation is available in .pdf here.

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