Geodesic
On stochastic models of service system with dependent process characteristics
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 110-139 
E. S. Kosarevskaya. On stochastic models of service system with dependent process characteristics. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 21, Tome 431 (2014), pp. 110-139. http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a7/
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     author = {E. S. Kosarevskaya},
     title = {On stochastic models of service system with dependent process characteristics},
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     pages = {110--139},
     year = {2014},
     volume = {431},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_431_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider a generalization of a service system model introduced by I. Kaj and M. Taqqu. Unlike their setting, we drop the unnatural assumption of independence between the duration and required resources quantity of a service process. We present a number of limit theorems for the process of integral workload. Wiener process, Fractional Brownian motion, or Stable Lévy process may show up as the limits.

[1] I. Kaj, M. S. Taqqu, “Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach”, In and Out of Equilibrium, v. 2, Ser. Progress in Probability, 60, Birkhäuser, Basel, 2008, 383–427 | MR | Zbl

[2] M. Lifshits, Random Processes by Example, World Scientific, Sigapure, 2014 | MR | Zbl

[3] K. A. Aksenova, “O stokhasticheskikh modelyakh teletrafika s tyazhëlymi khvostami raspredelenii”, Zap. nauchn. semin. POMI, 384, 2010, 5–20 | MR

[4] E. S. Garai, “O predelnoi teoreme v nekotorykh sistemakh obsluzhivaniya”, Zap. nauchn. semin. POMI, 431, 2014, 56–71

[5] D. V. Astakhova, Veroyatnosti bolshikh uklonenii v stokhasticheskikh modelyakh teletrafika, Diplomnaya rabota, SPbGU, 2011