Statistical Model of Network Traffic

I. Antoniou^1,2, V.V. Ivanov^1,3, Valery V. Ivanov^3,4 , P.V. Zrelov³

¹Solvay Institutes for Physics and Chemistry, Brussels, Belgium
²Aristoteles University of Thessaloniki, Thessaloniki, Greece
³Joint Institute for Nuclear Research, Dubna, Russia
⁴University Center, JINR, Dubna, Russia

A nonlinear analysis has been applied to traffic measurements obtained at the input of a medium size LAN [1]. Reliable values of the time lag and the embedding dimension provided a possibility to reconstruct the underlying dynamical system applying an artificial neural network (ANN). The ANN reproduced the statistical distribution of real data, which fits well the log-normal form. The detailed analysis of traffic measurements has shown that the log-normal distribution appears due to aggregation of real data [2]. The Principal Component Analysis of traffic series demonstrated that the first few components already form the main contribution to network traffic, while the residual components play a role of small irregular variations that can be interpreted as stochastic noise [3]. This result has also been confirmed by the application of wavelet filtering and Fourier analysis both to original traffic measurements and to individual principal components of original and filtered data [4]. The applicability of the A.Kolmogorov scheme [5] for homogeneous fragmentation of grains to network traffic is discussed.

[1] P.Akritas, P.G.Akishin, I.Antoniou, A.Yu.Bonushkina, I.Drossinos, V.V.Ivanov, Yu.L.Kalinovsky and P.V.Zrelov: Nonlinear Analysis of Network Traffic, "Chaos, Solitons and Fractals", Vol.14(4)(2002)595-606.
[2] I.Antoniou, V.V.Ivanov, Valery V.Ivanov and P.V.Zrelov: On a Log-Normal Distribution of Network Traffic, Physica D, 167(2002)72-85.
[3] I.Antoniou, V.V.Ivanov, Valery V.Ivanov and P.V.Zrelov: Principal Component Analysis of Network Traffic, Int. Conf. MII 2003, 14-16 April 2003, Thessaloniki, Greece, 170-181.
[4] I.Antoniou, V.V.Ivanov, Valery V.Ivanov and P.V.Zrelov: Wavelet Filtering of Network Traffic Measurements, Physica A 324(2003)733-753.
[5] A.N.Kolmogorov: Uber das logarithmisch normale Verteilungsgesetz der Dimensionen der Teilchen bei Zerstuckelung, Dokl. Akad. Nauk SSSR, 31, 99-101, 1941.