Multi-channel queueing networks with interdependent input flows in heavy traffic
Authors:
E. O. Lebedev, O. A. Chechelnitsky and G. V. Livinska
Translated by:
N. N. Semenov
Journal:
Theor. Probability and Math. Statist. 97 (2018), 113-125
MSC (2010):
Primary 60K25, 90B15
DOI:
https://doi.org/10.1090/tpms/1052
Published electronically:
February 21, 2019
MathSciNet review:
3746003
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Additional Information
Abstract: A service process in a multi-channel stochastic network with interdependent input flows is considered. Such a model is used when analyzing computer or communication networks as well as in medicine and particle physics (high-energy physics). Under the assumption of the critical load, theorems on diffusion approximations are proved. The local characteristics of the diffusion process are expressed in terms of parameters of the network.
References
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References
- V. M. Vishnevskiy, Theoretical Foundations of Computer Networks Projecting, “Technosphera”, Moscow, 2003. (Russian)
- B. V. Gnedenko and I. N. Kovalenko, Introduction to Queueing Theory, “ComKniga”, Moscow, 2005. (Russian)
- V. A. Ivnitskiy, Theory of Queueing Networks, “Fizmatlit”, Moscow, 2004. (Russian)
- E. A. Lebedev and A. A. Chechelnitsky, Diffusion approximation of queueing networks of open type, Ukr. Math. J. 41 (1989), no. 1, 95–99. MR 986721
- E. A. Lebedev and G. Livinska, Gaussian approximation of multi-channel networks in heavy traffic, Commun. Comput. Inf. Sci. 356 (2013), 122–130.
- R. S. Grifiths and R. K. Milne, A class of bivariate Poisson process, J. Multivar. Anal. 8 (1978), no. 3, 380–396. MR 512608
- K. Kawamura, The structure of bivariate Poisson distribution, Kodai Mathematical Seminar, 1973, REP 25, 246–256. MR 0326800
- I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations, “Naukova Dumka”, Kiev, 1982.
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- E. A. Lebedev, On Markov property of multi-dimensional Gaussian processes, Bulletin of Kyiv University (2001), no. 4, 287–291. MR 1935951
- V. V. Anisimov and E. A. Lebedev, Stochastic Queueing Networks. Markov Models, “Lybid”, Kiev, 1992. (Russian)
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Additional Information
E. O. Lebedev
Affiliation:
Department of Applied Statistics, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv, 01601, Ukraine
Email:
leb@unicyb.kiev.ua
O. A. Chechelnitsky
Affiliation:
Department of Applied Statistics, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv, 01601, Ukraine
Email:
achechelnitski@gmail.com
G. V. Livinska
Affiliation:
Department of Applied Statistics, Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, Volodymyrs’ka Street, 64/13, Kyiv, 01601, Ukraine
Email:
livinskaav@gmail.com
Keywords:
Multi-channel network,
multi-dimensional Poisson input flow,
diffusion approximation,
uniform topology
Received by editor(s):
September 13, 2017
Published electronically:
February 21, 2019
Article copyright:
© Copyright 2019
American Mathematical Society
