On the Use of Fractional Brownian Motion in the Theory of Connectionless Networks

Abstrucl- An abstract model for aggregated connectionless traffic, based on the fractional Brownian motion, is presented. Insight into the parameters is obtained by relating the model to an equivalent burst model. Results on a corresponding storage process are presented. The buffer occupancy distribution is approximated by a Weibull distribution. The model is compared with publicly available samples of real Ethernet traffic. The degree of the short-term predictability of the traffic model is studied through an exact formula for the conditional variance of a future value given the past. The applicability and interpretation of the self-similar model are discussed extensively, and the notion of ideal free traffic is introduced.

[1]  G. Gripenberg,et al.  On the prediction of fractional Brownian motion , 1996, Journal of Applied Probability.

[2]  Nick Duffield,et al.  Large deviations and overflow probabilities for the general single-server queue, with applications , 1995 .

[3]  Jorma T. Virtamo,et al.  The Superposition of Variable Bit Rate Sources in an ATM Multiplexer , 1991, IEEE J. Sel. Areas Commun..

[4]  Lajos Takács,et al.  Combinatorial Methods in the Theory of Stochastic Processes , 1967 .

[5]  Parag Pruthi,et al.  An application of deterministic chaotic maps to model packet traffic , 1995, Queueing Syst. Theory Appl..

[6]  Henry J. Fowler,et al.  Local Area Network Traffic Characteristics, with Implications for Broadband Network Congestion Management , 1991, IEEE J. Sel. Areas Commun..

[7]  Darryl Veitch,et al.  Novel models of broadband traffic , 1993, Proceedings of GLOBECOM '93. IEEE Global Telecommunications Conference.

[8]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[9]  V. E. Beneš,et al.  General Stochastic Processes in the Theory of Queues , 1965 .

[10]  S. V. Fomin,et al.  Ergodic Theory , 1982 .

[11]  Stamatis Cambanis,et al.  Stochastic and multiple Wiener integrals for Gaussian processes , 1978 .

[12]  M. Taqqu,et al.  Using Renewal Processes to Generate Long-Range Dependence and High Variability , 1986 .

[13]  J. Lamperti.  Semi-stable stochastic processes , 1962 .

[14]  Walter Willinger,et al.  On the self-similar nature of Ethernet traffic , 1993, SIGCOMM '93.