On stochastic models of teletraffic with heavy-tailed distributions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 5-20
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Following the approach suggested by I. Kaj and M. Taqqu, we consider a stochastic model of teletraffic based on Poisson random measure. We show that under appropriate assumptions the finite-dimensional distributions for the scaled workload process converge to those of a stable Lévy process. Bibl. 10 titles.
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K. A. Aksenova. On stochastic models of teletraffic with heavy-tailed distributions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 16, Tome 384 (2010), pp. 5-20. http://geodesic.mathdoc.fr/item/ZNSL_2010_384_a0/

[1] H. Biermé, A. Estrade, “Poisson random balls: self-similarity and $x$-ray images”, Adv. Appl. Probab., 38 (2006), 853–872 | DOI | MR | Zbl

[2] H. Biermé, A. Estrade, I. Kaj, “About scaling behavior of random balls models”, Proc. Conf. 6th International Conference on Stereology, Spatial Statistics, and Stochastic Geometry, 2006

[3] H. Biermé, A. Estrade, I. Kaj, “Scaling properties of Poisson germ-grain models with power-law grain size”, Proc. Conf. Russian–Scandinavian Symposium: Probability and Applied Probability, Petrozavodsk, 2006

[4] H. Biermé, A. Estrade, I. Kaj, “Self-similar random fields and rescaled random balls models”, J. Theoret. Probab. (to appear)

[5] J.-Ch. Breton, C. Dombry, “Rescaled weighted ranom balls models and stable self-similar random fields”, Stoch. Proc. Appl., 119 (2009), 3633–3652 | DOI | MR | Zbl

[6] I. Kaj, M. Taqqu, “Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach”, In and out of Equilibrium, v. II, Progress in Probability, 60, 2008, 383–427 | MR | Zbl

[7] I. Kaj, L. Leskelä, I. Norros, V. Schmidt, “Scaling limits for random fields with long-range dependence”, Ann. Probab., 35 (2007), 528–550 | DOI | MR | Zbl

[8] W. A. Rosenkrantz, J. Horowitz, “The infinite sourse model for internet traffic: statistical analysis and limit theorems”, Methods Appl. Analysis, 9 (2002), 445–462 | DOI | MR

[9] W. Willinger et al., “Long range dependence and data network traffic”, Theory and Applications of Long-Range Dependence, Birkhäuser, Basel, 2003 | MR | Zbl

[10] M. A. Lifshits, Materialy spetsseminara po teorii veroyatnostei, Preprint, SPbGU, 2009