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Usage of Modern Exponential-Smoothing Models in Network Traffic Modelling

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Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 210))


The article summarized current state of our works regarding usage of exponential smoothing Holt-Winters’ based models for analysis, modelling and forecasting Time Series with data of computer network traffic. Especially we use two models proposed by J. W. Taylor to deal with double and triple seasonal cycles for modelling network traffic in two local area networks and three campus networks. We use three time series with data of TCP, UDP and ICMP traffic (given by number of packets per interval) on each network.

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  1. Breunig, M.M., Kriegel, H.-P., Ng, R.T., Sander, J.: LOF: identifying density-based local outliers. In: ACM SIGMOD Conference Proceedings, pp. 93–104 (May 2000)

    Google Scholar 

  2. Brutlag, J.D.: Aberrant behavior detection in time series for network monitoring. In: Proceedings of the 14th System Administration Conference, New Orleans, Fla, USA, pp. 139–146 (2000)

    Google Scholar 

  3. Burkom, H.S., Murphy, S.P., Shmueli, G.: Automated time series forecasting for biosurveillance. Statist. Med. 26, 4202–4218, doi:10.1002/sim.2835

    Google Scholar 

  4. Chakhchoukh, Y., Panciatici, P., Bondon, P.: Robust estimation of SARIMA models: Application to short-term load forecasting. In: IEEE/SP 15th Workshop on Statistical Signal Processing, SSP 2009, August 31-September 3, pp. 77–80 (2009)

    Google Scholar 

  5. Chuah, M.C., Fu, F.: ECG Anomaly Detection via Time Series Analysis. In: Thulasiraman, P., He, X., Xu, T.L., Denko, M.K., Thulasiram, R.K., Yang, L.T. (eds.) ISPA 2007 Workshops. LNCS, vol. 4743, pp. 123–135. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Cordeiro, C., Neves, M.M.: Forecasting with exponential smoothing methods and bootstrap,

  7. Guzik, B., Appenzeller, D., Jurek, W.: Prognozowanie i symulacje. Wybrane zagadnienia, Wydawnictwo AE w Poznaniu, Poznań (2004)

    Google Scholar 

  8. Hanzák, T.: Holt-Winters method with general seasonality,

  9. Hanzák, T., Cipra, T.: Exponential smoothing for time series with outliers,

  10. Hao, M.C., Keim, D.A., Dayal, U., Schneidewind, J.: Business Process Impact Visualization and Anomaly Detection,

  11. Hauskrecht, et. al.: Evidence-based anomaly detection in clinical domains. In: Proceedings of the Annual American Medical Informatics Association (AMIA) Symposium (2007),

  12. Knorr, E.M., Ng, R.T., Tucakov, V.: Distance-Based Outliers: Algorithms and Applications. VLDB Journal 8(3-4), 237–253 (2000)

    Article  Google Scholar 

  13. Kratz, L., Nishino, K.: Anomaly Detection in Extremely Crowded Scenes Using Spatio-Temporal Motion Pattern Models, Department of Computer Science. Drexel University,

  14. Lawton, R.: On the Stability of the Double Seasonal Holt-Winters Method. University of the West of England,

  15. Wang, L., ,Zhang, R.-Q., Sheng, W., Xu, Z.-G.: Regression Forecast and Abnormal Data Detection Based on Support Vector Regression,

  16. Liu, W., Lin, S., Piegorsch, W.W.: Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model. International Statistical Review 76(1), 39–57, doi:10.1111/j.1751-5823.2007.00027.x

    Google Scholar 

  17. Markou, M., Singh, S.: Novelty detection: a review part 1: statistical approaches. Signal Processing 83, 2481–2497 (2003)

    Article  MATH  Google Scholar 

  18. Maronna, R., Martin, R.D., Yohai, V.: Robust Statistics - Theory and Methods. Wiley (2006)

    Google Scholar 

  19. Rivlin, A.E., Shimshoni, I.: Ror: Rejection of outliers by rotations in stereo matching. In: Conference on Computer Vision and Pattern Recognition (CVPR 2000), pp. 1002–1009 (June 2000)

    Google Scholar 

  20. Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley (1987) (republished in paperback, 2003)

    Google Scholar 

  21. Szmit, M., Adamus, S., Bugała, S., Szmit, A.: Implementation of Brutlag’s algorithm in Anomaly Detection 3. In: Federated Conference on Computer Science and Information Systems, Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 685–691. PTI, IEEE, Wrocław (2011)

    Google Scholar 

  22. Szmit, M., Szmit, A.: Use of holt-winters method in the analysis of network traffic: Case study. In: Kwiecień, A., Gaj, P., Stera, P. (eds.) CN 2011. CCIS, vol. 160, pp. 224–231. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  23. Szmit, M., Szmit, A.: Usage of Modified Holt-Winters Method in the Anomaly Detection of Network Traffic: Case Studies. Journal of Computer Networks and Communications 2012, doi:10.1155/2012

    Google Scholar 

  24. Szmit, M., Szmit, A.: Usage of Pseudo-estimator LAD and SARIMA Models for Network Traffic Prediction. Case Studies, Communications in Computer and Information Science 291, 229–236 (2012), doi:10.1007/978-3-642-31217-5_25

    Article  Google Scholar 

  25. Taylor, J.W.: Short-Term Electricity Demand Forecasting Using Double Seasonal Exponential Smoothing. Journal of Operational Research Society 54, 799–805 (2003),

    Article  MATH  Google Scholar 

  26. de la Torre, F., Black, M.J.: Robust principal component analysis for computer vision. In: Proceedings of the Eighth International Conference on Computer Vision (ICCV 2001), pp. 362–369 (2001)

    Google Scholar 

  27. Vala, R., Malaník, D., Jašek, R.: Usability of software intrusion-detection system in web applications. In: Herrero, Á., Snášel, V., Abraham, A., Zelinka, I., Baruque, B., Quintián, H., Calvo, J.L., Sedano, J., Corchado, E. (eds.) Int. JointConf. CISIS’12-ICEUTE’12-SOCO’12. AISC, vol. 189, pp. 159–166. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  28. Szmit, A., Szmit, M.: O wykorzystaniu modeli ekonometrycznych do prognozowania ruchu sieciowego, Zarządzanie rozwojem organizacji, Spała (accepted for publication, 2013)

    Google Scholar 

  29. ITU-T Recommendation E.490.1: Overview of Recommendations on traffic engineering, ITU (2003),

  30. ITU-T E.507 Models for Forecasting International Traffic, ITU (1998),

  31. Goodwin, P.: The Holt-Winters Approach to Exponential Smoothing: 50 Years Old and Going Strong, FORESIGHT Fall pp. 30–34 (2010),

  32. Taylor, J.W.: Exponentially Weighted Methods for Forecasting Intraday Time Series with Multiple Seasonal Cycles. International Journal of Forecasting 26, 627–646 (2010),

    Article  Google Scholar 

  33. Szmit, M.: Využití nula-jedničkových modelů pro behaviorální analýzu síťového provozu, Internet, competitiveness and organizational security, TBU, Zlín (2011)

    Google Scholar 

  34. Gelper, S., Fried, R., Croux, C.: Robust forecasting with exponential and Holt-Winters smoothing, Leuven (2007),

  35. Szmit, M., Szmit, A., Adamus, S., Bugała, S.: Usage of Holt-Winters Model and Multilayer Perceptron in Network Traffic Modelling and Anomaly Detection. Informatica 36(4), 359–368

    Google Scholar 

  36. Münz, G.: Traffic Anomaly Detection and Cause Identification Using Flow-Level Measurements, TUM, Müchen (2010),

  37. Wang, Y.: Statistical Techniques for Network Security: Modern Statistically-Based Intrusion Detection and Protection. IGI Global (2009)

    Google Scholar 

  38. Palmieri, F., Fiore, U.: Network anomalny detection though nonlinear analysis. Computers and Security 29, 737–755 (2010)

    Article  Google Scholar 

  39. Grzenda, M., Macukow, B.: Heat Consumption Prediction with Multiple Hybrid Models. In: Omatu, S., Rocha, M.P., Bravo, J., Fernández, F., Corchado, E., Bustillo, A., Corchado, J.M. (eds.) IWANN 2009, Part II. LNCS, vol. 5518, pp. 1213–1221. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  40. Villén-Altamirano, M.: Overview of ITU Recommendations on Traffic Engineering. Paper presented in the ITU/ITC workshop within 17th ITC

    Google Scholar 

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Correspondence to Roman Jašek .

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Jašek, R., Szmit, A., Szmit, M. (2013). Usage of Modern Exponential-Smoothing Models in Network Traffic Modelling. In: Zelinka, I., Chen, G., Rössler, O., Snasel, V., Abraham, A. (eds) Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 210. Springer, Heidelberg.

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  • Print ISBN: 978-3-319-00541-6

  • Online ISBN: 978-3-319-00542-3

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