The chaotic nature of TCP congestion control

Abstract

Abstract-In this paper we demonstrate how TCP congestion control can show chaotic behavior. We demonstrate the major features of chaotic systems in TCPlIP networks with examples. These features include unpredictability, extreme sensitivity to initial conditions and odd periodicity. Previous work has shown the fractal nature of aggregate TCPAP traffic and one explanation to this phenomenon was that traffic can be approximated by a large number of ON/OFF sources where the random ON and/or OFF periods are of length described by a heavy tailed distribution. In this paper we show that this argument is not necessary to explain selfsimilarity, neither randomness is required. Rather, TCP itself as a deterministic process creates chaos, which generates self-similarity. This property is inherent in todays TCPlIP networks and it is independent of higher layer applications or protocols. The two causes: heavy tailed ONlOFF and chaotic TCP together contribute to the phenomena, called fractal nature of Internet traffic.

Comparison-Based FIFO Buffer Management in QoS Switches

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“…Nonequilibrium fluctuations in queue behavior has been observed both experimentally and numerically [25], [27]. For appropriate parameter values, the simplified fluid models also exhibit persistent non-equilibrium behavior [3], [22], [28]. The nonequilibrium behavior in queues may be due to random noise or could arise as self-excited "chaotic oscillations" and there are suggestions for both in the literature [27].…”

“…Papers concerned with deriving mean or limit models [23], [29], [30], obtaining AQM performance with linear control methods [11], [31], or with carrying out describing function based analysis [32] typically assume a random noise. The papers concerned with local instability/bifurcation analysis [22], [33]- [36], and (global) numerical investigations [1], [3], [22] using deterministic fluid models show these oscillations as self-excited. With simple fluid models, analytical methods from bifurcation theory have been used to show that these self-excited oscillations can arise as a result of supercritical Hopf bifurcation [33], [35], [37] and of period doubling and border-collision bifurcations [22].…”

“…For instance, the chaotic oscillations have been typically studied using numerical simulations as in [3], [22]. Stochastic methods, on the other hand, enable analysis of the asymptotic chaotic dynamics in terms of invariant measures [38].…”

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