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Theory of Probability and Mathematical Statistics

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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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 97 (2017).
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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Abstract | References | Similar Articles | 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.


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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

DOI: https://doi.org/10.1090/tpms/1052
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