On the Cause and Effect of Self-Similar Network Traffic

This is a paper coauthored by Kihong Park, Keith (Gi) Kim, and Mark Crovella.

Abstract

In this work, we investigate the phenomenon of self-similar network traffic with respect to its cause and effect, with some implications to controllability. First, we identify a ``structural'' cause for network traffic self-similarity in the context of a client/server network environment. File size distribution on server nodes is shown to directly influence link-level self-similarity, and we quantify the degree to which heavy-tailedness of file size distribution affects observed self-similarity. This relationship is shown to be robust with respect to reliable and unreliable communication, change in network resources, and traffic mixing with well-behaved cross-traffic. The transport layer of the protocol stack is shown to exert a significant influence on the long-range dependency of downstream traffic via its reliability mechanism which, in some sense, is crucial to its very realization. We show that in a network model with bounded resources and coupling among traffic sources through resource contention, the influence of heavy-tailed filesize distribution is strong enough to generate self-similarity regardless of the nature of the idle time distribution--heavy-tailed or non-heavy-tailed. Functionally dependent variables such as packet loss at bottleneck links are also shown to exhibit scale-invariant variability.

Second, we study the effect of self-similarity on network performance including its effect on packet loss, retransmission rate, mean queue length, and reliable transmission time. Scale-invariant burstiness is shown to lead to deterioration in performance across all the measured indicators, with mean queue length being the most sensitive. Although packet loss rate increases superlinearly with increasing self-similarity when an unreliable UDP-like transport protocol is employed, under reliable communication using TCP Reno, performance degradation is graceful showing a roughly linear decline in performance. This resiliency, however, is achieved at the expense of a disproportionate consumption of buffer space consistent with the observation that queue length distribution under self-similar traffic is more slowly decaying than with Poisson sources. A similarly graded relation ship is shown to hold as a function of bottleneck bandwidth and buffer space when using reliable packet transport.

We conclude with a discussion of issues related to controllability of self-similar traffic, in particular, as it pertains to observability and time-scale. We find that quantitative differences in aggregated traffic burstiness between self-similar and smooth traffic which depend on bottleneck bandwidth, becoming finer as the latter is increased. On-line ``detectable'' (e.g., through time-outs) events such as packet loss, however, seem to set in with discernible effect at time scales higher than that of throughput, suggesting possible limitations for congestion control to achieve increased effectiveness without exercising control at commensurate time-scales.