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On a lower asymptotic bound of the overflow probability in a fluid queue with a heterogeneous fractional input. (English) Zbl 07084326
Summary: For a fluid queue fed by superposition of fractional Brownian motion and alpha-stable Lévy process, the asymptotic lower bound of the overflow probability is obtained.
MSC:
60 Probability theory and stochastic processes
68 Computer science
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[1] Breiman, L., On some limit theorems similar to the arc-sin law, Theor. Probab. Appl., 10, 323-331, (1965) · Zbl 0147.37004
[2] Cline, DBH; Samorodnitsky, G., Subexponentiality of the product of independent random variables, Stoch. Proc. Appl., 49, 75-98, (1994) · Zbl 0799.60015
[3] P. Embrechts and M. Maejima, Selfsimilar Processes, Prinston University Press (2002).
[4] I. Kaj, Stochastic Modeling in Broadband Communications Systems, SIAM, Philadelphia (2002). · Zbl 1020.94001
[5] Leland, W.; Taqqu, M.; Willinger, W.; Wilson, D., On the selfsimilar nature of Ethernet traffic (extended version), IEEE/ACM Trans. Netw., 2, 1-15, (1994)
[6] M. Mandjes, Large Deviations of Gaussian Queues, Wiley, Chichester (2007). · Zbl 1125.60103
[7] Mikosch, T.; Resnick, S.; Rootzen, H.; Stegeman, A., Is network traffic approximated by stable Lévy motion or fractional Brownian motion?, Ann. Appl. Probab., 12, 23-68, (2002) · Zbl 1021.60076
[8] Norros, I., A storage model with self-similar input, Queuing Syst., 16, 387-396, (1994) · Zbl 0811.68059
[9] Reich, E., On the integrodifferential equation of Takacs I, Ann. Math. Stat., 29, 563-570, (1958) · Zbl 0086.33703
[10] G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes, Chapman and Hall (1994). · Zbl 0925.60027
[11] S. Sarvotham, R. Riedi, and R. Baraniuk, Connection-level analysis and modeling of network traffic, Tech. Rep., ECE Dept., Rice Univ. (2001).
[12] S. Sarvotham, R. Riedi, and R. Baraniuk, “Connection-level analysis and modeling of network traffic,” in: Proceedings of the 1st ACM SIGCOMM Workshop on Internet Measurement, ACM, New York (2001), pp. 99-103.
[13] I. V. Shmelev, “Vliyanie fraktal’nykh protsessov na setevoi teletrafik v sovremennykh raspredelennykh informatsionnykh setyakh,” in: Reinzhiniring Biznes-protsessov na Osnove Informatsionnykh Tekhnologii, Mosk. Gosud. Universitet ekonomiki, statistiki i informatiki, Moscow (2004), pp. 11-12.
[14] I. V. Shmelev, “Model’ trafika mul’tiservisnoi seti na osnove smesi samopodobnykh protsessov,” in: Mezhdunarodnyi Forum Informatizatsii MFI-2004, MTUSI, Moscow (2004), p. 12
[15] I. I. Tsitovich, “Ustoichivye modeli trafika mul’tiservisnykh setei,” in: Trudy Rossiiskogo Nauchno-Tekhnicheskogo Obshchestva Radiotekhniki, Elektroniki i Svyazi Imeni A.S.Popova. Seriya: Nauchnaya Sessiya, Posvyashchennaya Dnyu Radio, Vol. 2 (2005), pp. 271-273.
[16] V. M. Zolotarev, One-Dimensional Stable Distributions, AMS (1986).
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