Heavy-Tailed ON/OFF Source Behavior and Self-Similar Traffic

Recent traffic measurement studies suggest that the self-similarity observed in packet traffic arises from aggregating individual sources which behave in an ON/OFF manner with heavy-tailed sojourn times in one or both of the states. In this paper, we investigate the connection between general ON/OFF behavior, self-similarity and queueing performance. We use chaotic maps to model general ON/OFF behavior with combinations of heavy tailed and light tailed sojourn time behavior. We present results which show that chaotic maps which capture the heavytailed sojourn time behavior in the OFF and/or ON states generate traffic that is asymptotically self-similar. However, the resulting queue length distribution decays as a power law with the heavy ON source, and as an exponential with the light ON source, even though both processes exhibit identical 1/f noise behavior. To resolve this apparent paradox, we consider aggregates of ON and OFF sources, and show that the nature of the ON period is less consequential, and in both instances the aggregate appears to converge to Fractional Brownian Motion (FBM). The queueing behavior is heavy in both cases, corresponding to the “stretched exponential” form predicted by FBM models. This indicates that differences in the single source case arise due to the impacts of higher order statistics, which become less significant as sources are aggregated. Convergence to FBM is observed to be slower with light ON sources. Our results indicate that in assessing the impact of long range dependence on performance, the potential impacts of other factors, such as higher-order statistics, must also be considered. Further, our analysis indicates conditions under which long-range dependence can dominate queueing performance in fast packet and SS7 networks, and with Variable Bit Rate (VBR) video applications.