Abstract
Stochastic discrete-event simulation studies of communication networks often require a mechanism to transform self-similar processes with normal marginal distributions into self-similar processes with arbitrary marginal distributions. The problem of generating a self-similar process of a given marginal distribution and an autocorrelation structure is difficult and has not been fully solved. Our results presented in this paper provide clear experimental evidence that the autocorrelation function of the input process is not preserved in the output process generated by the inverse cumulative distribution function (ICDF) transformation, where the output process has an infinite variance. On the other hand, it preserves autocorrelation functions of the input process where the output marginal distributions (exponential, gamma, Pareto with α= 20.0, uniform and Weibull) have finite variances, and the ICDF transformation is applied to long-range dependent self-similar processes with normal marginal distributions.
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References
Law, A., Kelton, W.: Simulation Modeling and Analysis, 2nd edn. McGraw-Hill, Inc., Singapore (1991)
Jeong, H.D.: Modelling of Self-Similar Teletraffic for Simulation. PhD thesis, Department of Computer Science, University of Canterbury (2002)
Jeong, H.D., Lee, J.S., Park, H.W.: Teletraffic Generation of Self-Similar Processes with Arbitrary Marginal Distributions for Simulation: Analysis of Hurst Parameters. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds.) ICCSA 2004. LNCS, vol. 3045, pp. 827–836. Springer, Heidelberg (2004)
Melamed, B.: TES: a Class of Methods for Generating Autocorrelated Uniform Variates. ORSA Journal on Computing 3(4), 317–329 (1991)
Melamed, B., Hill, J.R.: A Survey of TES Modeling Applications. Simulation, 353–370 (1995)
Cario, M., Nelson, B.: Autoregressive to Anything: Time-Series Input Processes for Simulation. Operations Research Letters 19, 51–58 (1996)
Cario, M., Nelson, B.: Numerical Methods for Fitting and Simulating Autoregressive-to-Anything Processes. INFORMS Journal on Computing 10(1), 72–81 (1998)
Jeong, H.D., McNickle, D., Pawlikowski, K.: Generation of Self-Similar Time Series for Simulation Studies of Telecommunication Networks. In: Proceedings of the First Western Pacific and Third Australia-Japan Workshop on Stochastic Models in Engineering, Technology and Management, Christchurch, New Zealand, pp. 221–230 (1999)
Jeong, H.D., McNickle, D., Pawlikowski, K.: Generation of Self-Similar Processes for Simulation Studies of Telecommunication Networks. Mathematical and Computer Modelling 38(11-13), 1249–1257 (2003)
Paxson, V.: Fast, Approximate Synthesis of Fractional Gaussian Noise for Generating Self-Similar Network Traffic. Computer Communication Review, ACM SIGCOMM 27(5), 5–18 (1997)
Abry, P., Flandrin, P., Taqqu, M., Veitch, D.: Self-Similarity and Long-Range Dependence Through the Wavelet Lens. In: Birkhäuser, Doukhan, Oppenheim, Taqqu (eds.) Theory and Applications of Long-Range Dependence, Boston, MA, pp. 527–556 (2002)
Leroux, H., Hassan, M.: Generating Packet Inter-Arrival Times for FGN Arrival Processes. In: The 3rd New Zealand ATM and Broadband Workshop, Hamilton, New Zealand, pp. 1–10 (1999)
Leroux, H., Hassan, M., Egudo, R.: On the Self-Similarity of Packet Inter-Arrival Times of Internet Traffic. In: The 3rd New Zealand ATM and Broadband Workshop, Hamilton, New Zealand, pp. 11–19 (1999)
Geist, R., Westall, J.: Practical Aspects of Simulating Systems Having Arrival Processes with Long-Range Dependence. In: Joines, J.A., Barton, R.R., Kang, K., Fishwick, P.A. (eds.) Proceedings of the 2000 Winter Simulation Conference, Orlando, Florida, USA, pp. 666–674 (2000)
Huang, C., Devetsikiotis, M., Lambadaris, I., Kaye, A.: Modeling and Simulation of Self-Similar Variable Bit Rate Compressed Video: A Unified Approach. In: Computer Communication Review, Proceedings of ACM SIGCOMM 1995, vol. 25(4), pp. 114–125 (1995)
Beran, J.: Statistics for Long-Memory Processes. Chapman and Hall, New York (1994)
Wise, G., Traganitis, A., Thomas, J.: The Effect of a Memoryless Nonlinearity on the Spectrum of a Random Process. IEEE Transactions on Information Theory IT-23(1), 84–89 (1977)
Liu, B., Munson, D.: Generation of a Random Sequence Having a Jointly Specified Marginal Distribution and Autocovariance. IEEE Transactions on Acoustics, Speech and Signal Processing ASSP-30 (6), 973–983 (1982)
Geist, R., Westall, J.: Correlational and Distributional Effects in Network Traffic Models. Performance Evaluation 44, 121–138 (2001)
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Jeong, HD.J., Lee, JS.R. (2006). A Study on Transformation of Self-similar Processes with Arbitrary Marginal Distributions. In: Jesshope, C., Egan, C. (eds) Advances in Computer Systems Architecture. ACSAC 2006. Lecture Notes in Computer Science, vol 4186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11859802_12
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DOI: https://doi.org/10.1007/11859802_12
Publisher Name: Springer, Berlin, Heidelberg
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