Alocação de Taxa de Transmissão Utilizando Predição do Tráfego de Rede Baseada no Expoente de Lyapunov
Resumo
Esse artigo avalia o desempenho de algoritmos selecionados, desenvolvidos com o propósito de quantificar parâmetros referentes à teoria do caos, primeiramente descrevendo um procedimento padrão de análise e medida de dados experimentais que apresentam características não-lineares, dentro do espectro da Teoria do Caos e seus procedimentos mais notáveis, para introduzir um método de predição de tráfego e propor uma alocação dinâmica de taxa de transmissão para servidores de rede baseada no expoente de Lyapunov e no parâmetro de Hurst. Reconstruir o atrator, determinar dimensão de incorporação e dimensão de correlação, estimar o expoente de Lyapunov e o parâmetro de Hurst, prever o tráfego, e alocar a taxa de transmissão correspondente para os servidores de rede são os passos seguidos nessa análise.
Palavras-chave:
Dimensão de Correlação, Reconstrução do Espaço de Fase, Expoente de Lyapunov, Parâmetro de Hurst, Alocação Dinâmica de Recursos
Referências
Alves, P. (2019). Chaos in historical prices and volatilities with five-dimensional eucli-dean spaces.Chaos, Solitons & Fractals: X, 1:100002.
Alves, P., Duarte, L., and [da Mota], L. (2017). A new characterization of chaos from a time series. Chaos, Solitons & Fractals, 104:323 – 326.
Alves, P., Duarte, L., and [da Mota], L. (2018). Detecting chaos and predicting in dow jones index. Chaos, Solitons & Fractals, 110:232 – 238.
Berge, P., Pomeau, Y., and Vidal, C. (1987). Order Within Chaos. Wiley.
Coninck, Q. D., Baerts, M., Hesmans, B., and Bonaventure, O. (2016). CRAWDAD dataset uclouvain/mptcpsmartphone (v. 2016-03-04). Downloaded from https://crawdad.org/uclouvain/mptcp_smartphone/20160304.
Danzig, P., Mogul, J., Paxson, V., and Schwartz, M. (2000). The internet traffic archivedatasets. Downloaded fromhttp://ita.ee.lbl.gov/. traceset: combined. Último acesso em 09-22-2010.
Feng, H., Shu, Y., and Yang, O. W. (2009). Nonlinear analysis of wireless lan traffic. Nonlinear Analysis: Real World Applications, 10(2):1021 – 1028.
Fraser, A. M. and Swinney, H. L. (1986). Independent coordinates for strange attractors from mutual information. Phys. Rev. A, 33:1134–1140.
Gleick, J. (1987).Chaos: Making a New Science. Penguin Books, USA.
Grassberger, P. and Procaccia, I. (1983a). Characterization of strange attractors.
Grassberger, P. and Procaccia, I. (1983b). Measuring the strangeness of strange attractors. Physica D, 9:189.
Hurst, H. E. (1956). The problem of long-term storage in reservoirs. Hydrological Sciences Journal, 1(3):13–27.
Kantz, H. and Schreiber, T. (2004). Nonlinear time series analysis, volume 7. Cambridge university press.
Kaplan, D. T. and Glass, L. (1993). Coarse-grained embeddings of time series: randomwalks, gaussian random processes, and deterministic chaos. Physica D: NonlinearPhenomena, 64(4):431–454.
Leland, W. E., Taqqu, M. S., Willinger, W., and Wilson, D. V. (1994). On the self-similarnature of ethernet traffic (extended version).IEEE/ACM Transactions on Networking,2(1):1–15.
Liebert, W. and Schuster, H. G. (1989). Proper choice of the time delay for the analysis of chaotic time series. Physics Letters A, 142(2-3):107–111.
Liu, Y. and Zhang, J. (2016). Predicting traffic flow in local area networks by the largest lyapunov exponent. Entropy, 18(1):32.Lorenz, E. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences,20(2):130–148.
Lorenz, E. (1995).The Essence Of Chaos. Jessie and John Danz lectures. Taylor &Francis.
Mandelbrot, B. B. (1968). Noah, joseph, and operational hydrology. Water resources research. 4 (5) : 909-918 ; 1968.
Mandelbrot, B. B. (1997). The variation of certain speculative prices. In Fractals and scaling in finance, pages 371–418. Springer.
Mandelbrot, B. B. and Hudson, R. L. (2004).The misbehaviour of markets: a fractalview of risk, ruin and reward. Profile, London, UK.
Mañé, R. (1981). On the dimension of the compact invariant sets of certain non-linearmaps. Lecture Notes in Mathematics, Berlin Springer Verlag, 898:230.
mirwais (2020). Largest lyapunov exponent with rosenstein’s algorithm. MATLAB Central File Exchange. Retrieved February 13, 2020.
Prigogine, I. and Stengers, I. (1984).Order Out of Chaos Man’s New Dialogue withNature /Ilya Prigogine and Isabelle Stengers ; Foreword by Alvin Toffler. –. –. BantamBooks, 1984.
Rocha, F. G. C. (2016). Alocação de recursos em redes sem fio ofdm multiusuário utilizando modelagem multifractal adaptativa.
Rocha, F. G. C. and Teles, F. H. V. (2013). Adaptive rate control based on loss probability estimation considering a cascade based multifractal model for the network traffic. IJWMIP, 11.
Rosenstein, M. T., Collins, J. J., and Luca, C. J. D. (1993). A practical method forcalculating largest lyapunov exponents from small data sets.Physica D: NonlinearPhenomena, 65(1):117 – 134.
Silva, M. R. P. d. (2019).Propostas de um modelo para o tráfego de redes decomunicações e de funções de janela para o filtro fir utilizado na tecnologia f-ofdm.
Solis, P. (2007). Uma metodologia de engenharia de tráfego baseada na abordagem auto-similar para a caracterização de parâmetros e a otimização de redes multimídia.
Strogatz, S. (2012). Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life. Hyperion.
Strogatz, S. H. (2015).Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. CRC Press.
Takens, F. (1981). Detecting strange attractors in turbulence.Lecture Notes in Mathematics, Berlin Springer Verlag, 898:366.
Tempelman, J. R. and Khasawneh, F. A. (2020). A look into chaos detection through topological data analysis. Physica D: Nonlinear Phenomena, 406:132446.
Tian, Z. (2020). Chaotic characteristic analysis of network traffic time series at differenttime scales. Chaos, Solitons & Fractals, 130:109412.
Trinh, N. C. and Miki, T. (1999). Dynamic resource allocation for self-similar traffic in atm network. Fifth Asia-Pacific Conference on ... and Fourth Optoelectronics and Communications Conference on Communications,, 1:160–165 vol.1.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A. (1985). Determining lyapunov exponents from a time series.Physica D: Nonlinear Phenomena, 16(3):285 – 317
Alves, P., Duarte, L., and [da Mota], L. (2017). A new characterization of chaos from a time series. Chaos, Solitons & Fractals, 104:323 – 326.
Alves, P., Duarte, L., and [da Mota], L. (2018). Detecting chaos and predicting in dow jones index. Chaos, Solitons & Fractals, 110:232 – 238.
Berge, P., Pomeau, Y., and Vidal, C. (1987). Order Within Chaos. Wiley.
Coninck, Q. D., Baerts, M., Hesmans, B., and Bonaventure, O. (2016). CRAWDAD dataset uclouvain/mptcpsmartphone (v. 2016-03-04). Downloaded from https://crawdad.org/uclouvain/mptcp_smartphone/20160304.
Danzig, P., Mogul, J., Paxson, V., and Schwartz, M. (2000). The internet traffic archivedatasets. Downloaded fromhttp://ita.ee.lbl.gov/. traceset: combined. Último acesso em 09-22-2010.
Feng, H., Shu, Y., and Yang, O. W. (2009). Nonlinear analysis of wireless lan traffic. Nonlinear Analysis: Real World Applications, 10(2):1021 – 1028.
Fraser, A. M. and Swinney, H. L. (1986). Independent coordinates for strange attractors from mutual information. Phys. Rev. A, 33:1134–1140.
Gleick, J. (1987).Chaos: Making a New Science. Penguin Books, USA.
Grassberger, P. and Procaccia, I. (1983a). Characterization of strange attractors.
Grassberger, P. and Procaccia, I. (1983b). Measuring the strangeness of strange attractors. Physica D, 9:189.
Hurst, H. E. (1956). The problem of long-term storage in reservoirs. Hydrological Sciences Journal, 1(3):13–27.
Kantz, H. and Schreiber, T. (2004). Nonlinear time series analysis, volume 7. Cambridge university press.
Kaplan, D. T. and Glass, L. (1993). Coarse-grained embeddings of time series: randomwalks, gaussian random processes, and deterministic chaos. Physica D: NonlinearPhenomena, 64(4):431–454.
Leland, W. E., Taqqu, M. S., Willinger, W., and Wilson, D. V. (1994). On the self-similarnature of ethernet traffic (extended version).IEEE/ACM Transactions on Networking,2(1):1–15.
Liebert, W. and Schuster, H. G. (1989). Proper choice of the time delay for the analysis of chaotic time series. Physics Letters A, 142(2-3):107–111.
Liu, Y. and Zhang, J. (2016). Predicting traffic flow in local area networks by the largest lyapunov exponent. Entropy, 18(1):32.Lorenz, E. (1963). Deterministic nonperiodic flow. Journal of Atmospheric Sciences,20(2):130–148.
Lorenz, E. (1995).The Essence Of Chaos. Jessie and John Danz lectures. Taylor &Francis.
Mandelbrot, B. B. (1968). Noah, joseph, and operational hydrology. Water resources research. 4 (5) : 909-918 ; 1968.
Mandelbrot, B. B. (1997). The variation of certain speculative prices. In Fractals and scaling in finance, pages 371–418. Springer.
Mandelbrot, B. B. and Hudson, R. L. (2004).The misbehaviour of markets: a fractalview of risk, ruin and reward. Profile, London, UK.
Mañé, R. (1981). On the dimension of the compact invariant sets of certain non-linearmaps. Lecture Notes in Mathematics, Berlin Springer Verlag, 898:230.
mirwais (2020). Largest lyapunov exponent with rosenstein’s algorithm. MATLAB Central File Exchange. Retrieved February 13, 2020.
Prigogine, I. and Stengers, I. (1984).Order Out of Chaos Man’s New Dialogue withNature /Ilya Prigogine and Isabelle Stengers ; Foreword by Alvin Toffler. –. –. BantamBooks, 1984.
Rocha, F. G. C. (2016). Alocação de recursos em redes sem fio ofdm multiusuário utilizando modelagem multifractal adaptativa.
Rocha, F. G. C. and Teles, F. H. V. (2013). Adaptive rate control based on loss probability estimation considering a cascade based multifractal model for the network traffic. IJWMIP, 11.
Rosenstein, M. T., Collins, J. J., and Luca, C. J. D. (1993). A practical method forcalculating largest lyapunov exponents from small data sets.Physica D: NonlinearPhenomena, 65(1):117 – 134.
Silva, M. R. P. d. (2019).Propostas de um modelo para o tráfego de redes decomunicações e de funções de janela para o filtro fir utilizado na tecnologia f-ofdm.
Solis, P. (2007). Uma metodologia de engenharia de tráfego baseada na abordagem auto-similar para a caracterização de parâmetros e a otimização de redes multimídia.
Strogatz, S. (2012). Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life. Hyperion.
Strogatz, S. H. (2015).Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. CRC Press.
Takens, F. (1981). Detecting strange attractors in turbulence.Lecture Notes in Mathematics, Berlin Springer Verlag, 898:366.
Tempelman, J. R. and Khasawneh, F. A. (2020). A look into chaos detection through topological data analysis. Physica D: Nonlinear Phenomena, 406:132446.
Tian, Z. (2020). Chaotic characteristic analysis of network traffic time series at differenttime scales. Chaos, Solitons & Fractals, 130:109412.
Trinh, N. C. and Miki, T. (1999). Dynamic resource allocation for self-similar traffic in atm network. Fifth Asia-Pacific Conference on ... and Fourth Optoelectronics and Communications Conference on Communications,, 1:160–165 vol.1.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A. (1985). Determining lyapunov exponents from a time series.Physica D: Nonlinear Phenomena, 16(3):285 – 317
Publicado
30/06/2020
Como Citar
ROSA, Évelynn; ROCHA, Flávio.
Alocação de Taxa de Transmissão Utilizando Predição do Tráfego de Rede Baseada no Expoente de Lyapunov. In: WORKSHOP EM DESEMPENHO DE SISTEMAS COMPUTACIONAIS E DE COMUNICAÇÃO (WPERFORMANCE), 19. , 2020, Cuiabá.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2020
.
p. 73-84.
ISSN 2595-6167.
DOI: https://doi.org/10.5753/wperformance.2020.11107.
