Abstract
Important problems of correct organization of simulation experiments for calculating fractal queueing systems are considered. Fractal systems are described asymptotically by power laws of arrival interval distribution and service time of requests and are adequate mathematical models of network devices of telecommunication systems with fractal (self-similar) traffic. We propose an effective solution to the problem for the correct realization of heavy-tailed distributions. Accuracy control techniques for calculating fractal queues by means of consecutive or repeated “parallel” runs of simulation models are developed. The application examples of the developed methods are given.
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References
Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, D.V.: On the self-similar nature of Ethernet traffic. ACM/SIGCOMM Comput. Commun. Rev., pp. 146–155 (1993)
Czachorski, T., Domanska, J., Pagano, M.: On stochastic models of internet traffic. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) Information Technologies and Mathematical Modeling, vol. 564, pp. 289–303. Springer, Switzerland (2015)
Crovella, M.E., Lipsky, L.: Simulation with heavy-tailed workloads. In: Park, K., Willinger, W. (eds.) Self Similar Network Traffic and Performance Evaluation, pp. 89–100. Willey, New Jersey (2000)
Zadorozhnyi, V.N.: Fractal queues simulation peculiarities. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) Communications in Computer and Information Science, vol. 564, pp. 413–432. Springer, Switzerland (2015)
Kleinrock, L.: Queueing systems. In: Computer Applications, vol. 2, p. 576. Wiley Interscience, New York (1976)
Zwart, A.P.: Queueing systems with heavy tails, p. 227. Eindhoven University of Technology, Eindhoven (2001)
Asmussen, S., Binswanger, K., Hojgaard, B.: Rare events simulation for heavy-tailed distributions. Bernoulli 6(2), 303–322 (2000)
Boots, N.K., Shahabuddin, P.: Simulating GI/GI/1 queues and insurance risk processes with subexponential distributions. In: Proceedings of the 2000 Winter Simulation Conference, pp. 656–665 (2000). Unpublished manuscript, Free University, Amsterdam. Shortened Version
Zadorozhnyi, V.N.: Simulation modeling of fractal queues. In: Dynamics of Systems, Mechanisms and Machines (Dynamics), pp. 1–4, December 2014. doi:10.1109/Dynamics.7005703
Kleijnen, J.P.C.: Statistical Techniques in Simulation, Part 1. Marcel Dekker, New York (1974)
GPSS World reference manual: Minuteman Software, 5th Edn., Holly Springs, NC, U.S.A (2009)
Zadorozhnyi, V.N.: Realization of big samples in simulation of queueing systems in GRSS World. In: IMMOD 2015, Moskow, pp. 225–230 (2015). (in Russian)
Zadorozhnyi, V.N.: The improving of GPSS models accuracy by employing the random variables generator - “Mersene twister”. Omskiy nauchnyiy vestnik 1(145), 90–94 (2016). (in Russian)
Karpov, J.: Simulation Modeling of Systems. Introduction to Simulation in AnyLogic, vol. 5. BHV-Peterburg, St. Petersburg (2005)
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Zadorozhnyi, V.N., Zakharenkova, T.R. (2016). Methods of Simulation Queueing Systems with Heavy Tails. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2016. Communications in Computer and Information Science, vol 638. Springer, Cham. https://doi.org/10.1007/978-3-319-44615-8_33
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DOI: https://doi.org/10.1007/978-3-319-44615-8_33
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