Abstract
Traffic models have been at the core of teletraffic research for the last several decades because they have traditionally served as fundamental tools for network performance analysis. With the recent discovery of fractal characteristics of Internet traffic, the need for fractal traffic models that play beyond this traditional role has grown significantly. This is attributed to the fact that despite tremendous interests being focused on a wide variety issues dealing with this fractal nature of Internet traffic, there still remain much new knowledge yet to be gained for its implications for Internet traffic engineering. This requires the fractal traffic models that can quantitatively link the model parameters to the fractal statistics of Internet traffic so that a parameterizable, physical structure can be associated with the Traffic under study, rather than providing mainly qualitative and abstract explanations. To meet this daunting challenge, a library of traffic models based on Fractal Point Processes (FPPs) are described and analyzed. Compared to other fractal Traffic models, the FPPs have several key advantages. First, they yield a simple and effective traffic parameterization method that determines the model parameters from the first- and second-order statistics. This result allows for quantitatively understanding how model parameters are related to and control the range of time scales over which fractal behavior is dominant. Second, they reveal how session-level fractal dynamics such as session arrivals, duration, and volume affect packet-level fractal dynamics in a quantitative manner. Moreover, they are versatile and thus are able to capture a broad range of different fractal behaviors. Additional advantage of these models includes low modeling complexity, yielding high computational efficiency for running large-scale simulations. Demonstration of these benefits are provided based on simulation and characterization of two Web traces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P.Abry and P.Flandrin, “Point Processes, Long-Range Dependence, and Wavelets”, In Wavelets and Medicine and Biology, eds. A. Aldroubi and M. Unser, CRC Press, FL, 1996.
P.Abry and D.Veitch, “Wavelet Analysis of Long Range Dependent Traffic”, Trans. Info. Theory, 44:2 – 15, 1998.
J. Aracil, R. Edell, and P. Varaiya, “A Phenomenological Approach to Internet Traffic Self-Similarity”, Preprint, 1996.
K. C. Claffy, H.-W. Braun, and G. C. Polyzos, “A Parameterizable Methodology for Internet Traffic Flow Profiling”, IEEE JSAC, 13: 1481 – 1494, 1995.
D. R. Cox., “Long-Range Dependence”, A review. In H. A. David and H. T. Davis, editors, Statistics: An Appraisal, pages 55–74. The Iowa State University Press, Ames, Iowa, 1984.
M. Crovella and A. Bestavros, “Self-Similarity in World Wide Web Traffic: Evidence and Possible Causes”, IEEE/ACM Trans. Net., pages 835 – 846, 1997.
N. G. Duffield, “Economies of Scale in Queues with Sources Having Power-Law Large Deviation Scalings”, J. Appl. Prob., 33:840–857, 1996.
N. G. Duffield, J. T. Lewis, and N. O’Connell, “Predicting Quality of Service for Traffic with Long-Range Fluctuations”, In Proc. ICC, Seattle, WA, 1995.
A. Erramilli, O. Narayan, and W. Willinger, “Experimental Queueing Analysis with Long-Range Dependent Packet Traffic”, IEEE/ACM Trans. Net., 4: 209 – 223, 1996.
A. Erramilli, R. P. Singh, and P. Pruthi, “An Application of Deterministic Chaotic Maps to Model Packet Traffic”, Queueing Systems, 20: 171–206,1995.
A. Feldmann, A. Gilbert, P. Huang, and W. Willinger, “Dynamics of IP Traffic: A Study of the Role of Variability and the Impact of Control”, In Proc. ACM SIGCOMM, 1999.
L. Kleinrock, “Queueing Systems: Volume I”, John Wiley & Sons, 1975.
W-C. Lau, A. Erramilli, J. Wang, and W. Willinger, “Self-Similar Traffic Generation: The Random Midpoint Displacement Algorithm and its Properties”, In Proc. IEEE ICC, Seattle, WA, 1995.
S. Lowen, “Refractoriness-Modified Doubly Stochastic Poisson Point Process”, Technical Report 449-96-15, Cent., for Telecomm. Res., Columbia University, New York, 1996.
S. Lowen and M. Teich, “The Periodogram and Allan Variance Reveal Fractal Exponents Greater than Unity in Auditory-Nerve Spike Trains”, J. Acoust. Soc. Am., 1996.
S. B. Lowen and M. C. Teich, “Doubly Stochastic Poisson Point Process Driven by Fractal Shot Noise”, Phy. Rev. A, 43:4192–4215, 1991.
S. B. Lowen and M. C. Teich, “Estimation and Simulation of Fractal Stochastic Point Processes”, Fractals, 3:183–210, 1995.
Steve Lowen, “Fractal Point Process Simulation”, http://cordelia.mclean.org:8080/lowen/fspp_sim.html.
I. Norros, “A Storage Model with Self-Similar Input”, Queueing Systems, 16:387–396, 1994.
A. Papoulis, “Probability, Random Variables, and Stochastic Processes”, McGraw-Hill, New York, third edition, 1990.
V. Paxson, “Fast Approximation of Self-Similar Network Traffic”, Technical report, Lawrence Berkeley Laboratory, 1995. LBL-36750.
V. Paxson and S. Floyd, “Wide Area Traffic: The Failure of Poisson Modeling”, IEEE Trans. Net., 3:226–244, 1995.
S. Robert and J.-Y. LeBoudec, “Can Self-Similar Traffic Be Modeled by Markovian Processes?”, In B. Plattner, editor, Lecture Notes in Comp. Sci. (Proc. Int’l Zurich Seminar on Dig. Comm.), volume 1044. Springer-Verlag, 1996.
B. Ryu, “Fractal Network Traffic: From Understanding to Implications”, PhD thesis, Columbia University, 1996. Also in CTR Technical Report, CU/CTR/TR 448-96-14.
B. Ryu, “Fractal Network Traffic Modeling: Past, Present, and Future”, In Proc. 35th Allerton Conference on Communication, Control, and Computing, Univ. Illinois at Urbaba-Champaign, IL, 1997.
B. Ryu, “Modeling and Simulation of Broadband Satellite Networks: Part II— Traffic Modeling”, IEEE Comm. Soc. Mag., pages 48–56, July 1999.
B. Ryu and S. Lowen, “Point Process Models for Self-Similar Network Traffic, with Applications”, Stochastic Models, 14(3):735–761, 1998.
B. K. Ryu and A. Elwalid, “The Importance of Long-Range Dependence of VBR Video Traffic in ATM Traffic Engineering: Myths and Realities”, In Proc. ACM SIGCOMM, SanFrancisco, CA, 1996.
B.K. Ryu and S.B. Lowen, “Modeling, Analysis, and Generation of Self-Similar Traffic with the Fractal-Shot-Noise-Driven Poisson Process” In Proc. IASTED Modeling and Simulation, Pittsburgh, PA, 1995.
B. K. Ryu and S. B. Lowen, “Point Process Approaches to the Modeling and Analysis of Self-Similar Traffic: Part I — Model Construction”, In Proc. IEEE INFOCOM’96, SanFrancisco, CA, 1996.
A. Shaikh, J. Rexford, and K. Shin, “Load-Sensitive Routing of Long-Lived Ip Flows”, In Proc. ACM SIGCOMM, 1999.
M. S. Taqqu and J. B. Levy, “Using Renewal Processes to Generate Long-Range Dependence and High Variability”, In E. Eberlein and M. S. Taqqu, editors, Dependence in Probability and Statistics, volume 11, pages 73–89. Birkhauser, Boston, MA, 1986.
S. Thurner et al, “Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes”, Fractals, 5, 1997.
W. Willinger and V. Paxson, “Where Mathematics Meets the Internet”, Notices of the American Math. Soc., 45(8), aug 1998.
W. Willinger, M. Taqqu, R. Sherman, and D. Wilson, “Self-Similarity through High-Variability: Statistical Analysis of Eternet LAN Traffic at the Source Level”, In Proc. ACM SIGCOMM, Cambridge, MA, 1995.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ryu, B., Lowen, S.B. (2002). Fractal Traffic Model for Internet Traffic Engineering. In: Ince, A.N. (eds) Modeling and Simulation Environment for Satellite and Terrestrial Communications Networks. The Kluwer International Series in Engineering and Computer Science, vol 645. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0863-2_5
Download citation
DOI: https://doi.org/10.1007/978-1-4615-0863-2_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5276-1
Online ISBN: 978-1-4615-0863-2
eBook Packages: Springer Book Archive