Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 
 

 

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

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 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. Dvurechenski{\u{\i}}\kern.15em, 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. MR 87e:15001
  • 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. MR 42:3851
  • 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). MR 42:8547
  • 8. V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications, ``Naukova Dumka'', Kiev, 1976. (Russian) MR 54:8913

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60A25

Retrieve articles in all journals with MSC (2000): 60A25


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

DOI: https://doi.org/10.1090/S0094-9000-04-00606-4
Received by editor(s): December 10, 2001
Published electronically: June 10, 2004
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society