Abstract
Experimental measurements show that many relevant processes in telecommunication engineering exhibit self-similarity and long-range dependence (LRD) characteristics. Internet traffic is a significant example. A traditional parameter used to characterize self-similarity and LRD is the Hurst parameter H. Recently, the Modified Allan Variance (MAVAR) has been proposed to estimate the power-law spectrum and thus the Hurst parameter of LRD series. Chaotic generators have been introduced in the last years to mimic time series derived both from sampled Internet or packet video traffic. They are built by means of optimized weighted sums of geometric characteristic sampled from Lorenz strange attractors. The optimization of the structure is obtained observing both the variation coefficients (i.e., a traditional long term feature well matched to the analysis of the error gap processes, related to the Variance-Time plot and to the Hurst parameter too), and, more recently, the logscale diagram. Then, it was quite natural to explore the MAVAR characterization of time series derived from the above chaotic generators, and to compare it to that exhibited by the mimicked process, looking for a fruitful inclusion of MAVAR terms in the optimization cost function.
Work partially supported by the Italian Ministry of Education, University and Research (MIUR) under the FIRB project “TANGO” and the PRIN project “SHINES”.
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References
Park, K., Willinger, W. (eds.): Self Similar Network Traffic and Performance Evaluation. Wiley Interscience, Hoboken (2000)
Abry, P., Baraniuk, R., Flandrin, P., Riedi, R., Veitch, D.: The Multiscale Nature of Network Traffic: Discovery Analysis and Modelling. IEEE Signal Processing Magazine (April 2002)
Bregni, S.: Synchronization of Digital Telecommunication Networks. John Wiley and Sons, Chichester (March 2002)
Barnes, J.A., Chi, A.R., Cutler, L.S., Healey, D.J., Leeson, D.B., McGunigal, T.E., Mullen Jr., J.A., Smith, W.L., Sydnor, R.L., Vessot, R.F.C., Winkler, G.M.R.: Characterization of Frequency Stability. IEEE Trans. on Instr. and Meas. IM-20(2) (May 1971)
Allan, D.W., Barnes, J.A.: A Modified Allan Variance with Increased Oscillator Characterization Ability. In: Proc. of the 35th Annual Frequency Control Symposium (1981)
Bernier, L.G.: Theoretical Analysis of the Modified Allan Variance. In: Proc. of the 41st Annual Frequency Control Symposium (1987)
Lesage, P., Ayi, T.: Characterization of Frequency Stability: Analysis of the Modified Allan Variance and Properties of Its Estimate. IEEE Trans. On Instr. And Meas. IM-33(4) (December 1984)
Rutman, J., Walls, F.L.: Characterization of Frequency Stability in Precision Frequency Sources. Proc. of the IEEE 79(6) (1991)
Bregni, S., Primerano, L.: The modified Allan variance as time-domain analysis tool for estimating the Hurst parameter of long-range dependent traffic. In: IEEE GLOBECOM 2004, Dallas, TX, USA (2004)
Costamagna, E., Favalli, L., Gamba, P.: Multipath channel modeling with chaotic attractors. Proc. IEEE 90, 842–859 (2002)
Peitgen, H.O., Jurgens, H., Saupe, D.: Chaos and Fractals. New Frontiers of Science. Springer, Heidelberg (1992)
Kanal, L.N., Sastry, A.R.K.: Models for channels with memory and their application to error control. Proc. IEEE 66, 724–744 (1978)
Press, W.H., Teukolsky, S.A., Wetterling, W.T., Flannery, B.P.: Wetterling and B.P. Flannery, Numerical Recipes in FORTRAN, the Art of Scientific Computing. Cambridge University Press, Cambridge (1992)
Costamagna, E., Favalli, L., Tarantola, F.: Video traffic modeling in IP networks with hidden Markov models and chaotic attractors. In: Proc. of the 12th international Packetvideo Workshop, Pittsburgh, PA, April 24-26 (2002)
Costamagna, E., Favalli, L., Tarantola, F.: Chaos equation and hidden Markov models for packet video traffic simulation. In: Del Re, E. (ed.) Proc. of EMPS 2002, Baveno/Stresa, Italy, September 25-26 (2002)
Costamagna, E., Favalli, L., Tarantola, F.: Modeling and Analysis of Aggregate and Single Stream Internet Traffic. In: IEEE GLOBECOM 2003, San Francisco, CA, December 1-5 (2003)
Costamagna, E., Favalli, L., Savazzi, P., Tarantola, F.: Chaos model for sample time series and wavelet analysis. In: WPMC 2004, Abano Terme, Italy, September 12-15 (2004)
Rabiner, L.R.: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77, 257–286 (1989)
Turin, W., Sondhi, M.M.: Modeling error sources in digital channels. IEEE J. Select. Areas Commun. 11, 340–347 (1993)
Traffic trace repository is accessible at, http://tracer.csl.sony.co.jp (maintained by MAWI Working Group)
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Bregni, S., Costamagna, E., Erangoli, W., Favalli, L., Pattavina, A., Tarantola, F. (2005). Synthesis and MAVAR Characterization of Self-similar Traffic Traces from Chaotic Generators. In: Ajmone Marsan, M., Bianchi, G., Listanti, M., Meo, M. (eds) Quality of Service in Multiservice IP Networks. QoS-IP 2004. Lecture Notes in Computer Science, vol 3375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30573-6_7
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DOI: https://doi.org/10.1007/978-3-540-30573-6_7
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