A limit theorem for stochastic networks and its applications
Author:
E. O. Lebedev
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal:
Theor. Probability and Math. Statist. 68 (2004), 81-92
MSC (2000):
Primary 60A25
DOI:
https://doi.org/10.1090/S0094-9000-04-00606-4
Published electronically:
June 10, 2004
MathSciNet review:
2000397
Full-text PDF Free Access
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Abstract: A service process in an overloaded regime for multichannel stochastic networks is considered. A general functional limit theorem is proved, and the properties of the limit process are studied. An application of the approximation obtained is given for the case of networks with a semi-Markov input.
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1 W. A. Massey and W. Whitt, A stochastic model to capture space and time dynamics in wireless communication systems, Probability in the Engineering and Informational Sciences 8 (1994), 541–569.
2 A. Dvurechenskiĭ, L. A. Kulyukina, and G. A. Ososkov, Estimates of the Primary Ionization in Ionization Chambers, Preprint 5-81-362, Joint Institute for Nuclear Research, Dubna, 1981. (Russian)
3 I. I. Gikhman, A. V. Skorokhod, and M. I. Yadrenko, Probability Theory and Mathematical Statistics, “Vyshcha Shkola”, Kiev, 1988. (Russian)
4 A. A. Borovkov, Asymptotic Methods in the Queueing Theory, “Nauka”, Moscow, 1980; English transl., Wiley, New York, 1984.
5 R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
6 V. V. Anisimov, Limit theorems for semi-Markov processes with a finite phase space, Dokl. Akad. Nauk SSSR 193 (1970), no. 3, 503–505; English transl. in Soviet Math. Dokl. 11 (1970), 945–948.
7 D. S. Silvestrov, Limit theorems for functionals of step processes constructed from sums of random variables defined on a semi-Markov process with a finite phase space, Dokl. Akad. Nauk SSSR 195 (1970), no. 5, 1036–1038; English transl. in Soviet Math. Dokl. 11 (1971).
8 V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications, “Naukova Dumka”, Kiev, 1976. (Russian)
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Additional Information
E. O. Lebedev
Affiliation:
Department of Applied Statistics, Faculty for Cybernetics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 4, Kyiv–127 03127, Ukraine
Email:
leb@unicyb.kiev.ua
Received by editor(s):
December 10, 2001
Published electronically:
June 10, 2004
Article copyright:
© Copyright 2004
American Mathematical Society
