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Theory of Probability and Mathematical Statistics

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A limit theorem for non-Markovian multi-channel networks under heavy traffic conditions

Author: H. V. Livinska
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
Journal: Theor. Probability and Math. Statist. 93 (2016), 113-122
MSC (2010): Primary 60K25, 90B15
Published electronically: February 7, 2017
MathSciNet review: 3553444
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Abstract: Open multi-channel stochastic networks are considered in the paper. The inputs are assumed to be non-homogeneous Poisson flows whose rates depend on time. Service times are random variables whose distribution functions are of the GI-type. A limit theorem for the service process is proved for such a network under heavy traffic conditions. Characteristics of the limit Gaussian process are expressed in an explicit form in terms of the network parameters.

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Additional Information

H. V. Livinska
Affiliation: Department of Applied Statistics, Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue, 4D, Kyiv 03127, Ukraine

Keywords: Multi-channel queueing networks, diffusion approximation, heavy traffic regime
Received by editor(s): June 16, 2015
Published electronically: February 7, 2017
Additional Notes: This paper was prepared following the talk at the International conference “Probability, Reliability and Stochastic Optimization (PRESTO-2015)” held in Kyiv, Ukraine, April 7–10, 2015
Article copyright: © Copyright 2017 American Mathematical Society