TCP Congestion Control and Heavy Tails

Long-range dependence has been observed in many recent Internet traffic measurements. Previous studies have shown that there is a close relationship between heavy-tailed distribution of various traffic parameters and the long-range dependent property. In this paper, we use a simple Markov chain model to argue that when the loss rate is relatively high, TCP’s adaptive congestion control mechanism indeed generates traffic with heavy-tailed OFF, or idle, periods, and therefore introduces long-range dependence into the overall traffic. Moreover, the degree of such long-range dependence, measured by the Hurst parameter, increases as the loss rate increases, agreeing with many previous measurement-based studies. In addition, we observe that more variable initial retransmission timeout values for different packets introduces more variable packet inter-arrival times, which increases the burstiness of the overall traffic. Finally, we show that high loss conditions can lead to a heavy-tailed distribution of transmission times even for constant-sized files. This means that file size variability need not be the only cause of heavy-tailed variability in transmission durations. Keywords— Congestion Control, Long-Range Dependence, Self-Similarity.