Abstract
The aim of this paper is to use the superposition of two-state Markov Modulated Poisson Processes to replicate the statistical nature of internet traffic over several time scales. This paper characterizes of network traffic using Bellcore data and LAN traces collected in IITiS PAN. The fitting procedure for matching second-order self-similar properties of real data traces to that of two-state MMPP’s has also been described.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Kleinrock, L.: Queueing Systems, vol. II. Wiley, New York (1976)
Becchi, M.: From Poisson Processes to Self-Similarity: a Survey of Network Traffic Models. Technical report, Citeseer (2008)
Crovella, M., Bestavros, A.: Self-similarity in World Wide Web Traffic: Evidence and Possible Causes. IEEE/ACM Transactions on Networking 5, 835–846 (1997)
Domański, A., Domańska, J., Czachórski, T.: The impact of self-similarity on traffic shaping in wireless LAN. In: Balandin, S., Moltchanov, D., Koucheryavy, Y. (eds.) NEW2AN 2008. LNCS, vol. 5174, pp. 156–168. Springer, Heidelberg (2008)
Paxson, V., Floyd, S.: Wide area traffic: the failure of poisson modeling. IEEE/ACM Transactions on Networking 3, 226–244 (1995)
Willinger, W., Leland, W.E., Taqqu, M.S.: On the self-similar nature of ethernet traffic. IEEE/ACM Transactions on Networking 2, 1–15 (1994)
Garret, M., Willinger, W.: Analysis, modeling and generation of self-similar VBR video traffic. In: ACM SIGCOMM, London, pp. 269–280 (1994)
Norros, I.: On the use of fractional Brownian motion in the theory of connectionless networks. IEEE Journal on Selected Areas in Communication 13(6), 953–962 (1995)
Taqqu, M.S., Willinger, W., Sherman, R.: Proof of a fundamental result in self-similar traffic modeling. Computer Communication Review 27(2), 5–23 (1997)
Mikosch, T., Resnick, S., Rootzen, H., Stegeman, A.: Is Network Traffic approximated by Stable Levy Motion or Fractional Brownian Motion? The Analysis of Applied Probability 12(1), 23–68 (2002)
Erramilli, A., Singh, R.P., Pruthi, P.: An Application of Determinic Chaotic Maps to Model Packet Traffic. Queueing Systems 20(1-2), 171–206 (1995)
Gallardo, J.R., Makrakis, D., Orozco-Barbosa, L.: Use a α-stable self-similar stochastic processes for modeling traffic in broadband networks. Performance Evaluation 40(1-3), 71–98 (2000)
Harmantzis, F., Hatzinakos, D.: Heavy network traffic modeling and simulation using stable FARIMA processes. In: 19th International Teletraffic Congress, Beijing, China (2005)
Laskin, N., Lambadatis, I., Harmantzis, F.C., Devetsikiotis, M.: Fractional Levy Motion and its Application to network traffic modeling. Computer Networks 40(3), 363–375 (2002)
Robert, S., Boudec, J.Y.L.: New models for pseudo self-similar traffic. Performance Evaluation 30(1-2), 57–68 (1997)
Muscariello, L., Mellia, M., Meo, M., Ajmone Marsan, M., Lo Cigni, R.: Markov models of internet traffic and a new hierarchical MMPP model. Computer Communications 28, 1835–1851 (2005)
Clegg, R.G.: Markov-modulated on/off processes for long-range dependent internet traffic. Computing Research Repository, CoRR, arXiv:cs/0610135 (2006)
Domańska, J., Domański, A., Czachórski, T.: The Drop-From-Front Strategy in AQM. In: Koucheryavy, Y., Harju, J., Sayenko, A. (eds.) NEW2AN 2007. LNCS, vol. 4712, pp. 61–72. Springer, Heidelberg (2007)
Domańska, J., Domański, A., Czachórski, T.: Internet traffic source based on Hidden Markov Model. In: Balandin, S., Koucheryavy, Y., Hu, H. (eds.) NEW2AN/ruSMART 2011. LNCS, vol. 6869, pp. 395–404. Springer, Heidelberg (2011)
Domańska, J., Augustyn, D.R., Domański, A.: The choice of optimal 3-rd order polynomial packet dropping function for NLRED in the presence of self-similar traffic. Bulletin of the Polish Academy of Sciences, Technical Sciences 60(4) (2012)
Andersen, A.T., Nielsen, B.F.: A Markovian Approach for Modeling Packet Traffic with Long-Range Dependence. IEEE Journal on Selected Areas in Communications 16(5) (1998)
Bellcore Morristown Research and Engineering facility traffic traces, http://ita.ee.lbl.gov/html/contrib/BC.html
Foremski, P., Callegari, C., Pagano, M.: Waterfall: Rapid identification of IP flows using cascade classification. In: Kwiecień, A., Gaj, P., Stera, P. (eds.) 21th Conference on Computer Networks, CN 2014. CCIS, vol. 431, pp. 14–23. Springer, Heidelberg (2014)
Mandelbrot, B., Ness, J.V.: Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review 10 (October 1968)
Bhattacharjee, A., Nandi, S.: Statistical analysis of network traffic inter-arrival. In: 12th International Conference on Advanced Communication Technology, USA, pp. 1052–1057 (2010)
Cox, D.R.: Long-range dependance: A review. In: Statistics: An Appraisal, pp. 55–74 (1984)
Beran, J.: Statistics for Long-Memory Processes. Chapman and Hall (1994)
Stallings, W.: High-Speed Networks: TCP/IP and ATM Design Principles. Prentice-Hall (1998)
Casale, G.: Building accurate workload models using Markovian Arrival Processes. In: SIGMETRICS 2011, San Jose, USA (June 2011)
Fischer, W., Meier-Hellstern, K.: The Markov-modulated Poisson process (MMPP) cookbook. Performance Evaluation 18(2), 149–171 (1993)
Okamura, H., Kamahara, Y., Dohi, T.: Estimating Markov-modulated compound poisson processes. In: Valuetools 2007, Nantes, France (October 2007)
Domańska, J., Domański, A.: The influence of traffic self-similarity on QoS mechanism. In: International Symposium on Applications and the Internet, SAINT, Trento, Italy (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Domańska, J., Domański, A., Czachórski, T. (2014). Modeling Packet Traffic with the Use of Superpositions of Two-State MMPPs. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2014. Communications in Computer and Information Science, vol 431. Springer, Cham. https://doi.org/10.1007/978-3-319-07941-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-07941-7_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07940-0
Online ISBN: 978-3-319-07941-7
eBook Packages: Computer ScienceComputer Science (R0)