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On Gaussian Approximation of Multi-Channel Networks with Input Flows of General Structure

  • E. O. Lebedev
  • H. V. LivinskaEmail author
  • J. Sztrik
Article

In this paper, a multi-channel queueing network with input flow of a general structure is considered. The multi-dimensional service process is introduced as the number of customers at network nodes. In the heavy-traffic regime, a functional limit theorem of diffusion approximation type is proved under the condition that the input flows converge to their limits in the uniform topology. A limit Gaussian process is constructed and its correlation characteristics are represented explicitly via the network parameters. A network with nonhomogeneous Poisson input flow is studied as a particular case of the general model, and a correspondent Gaussian limit process is built.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Taras Shevchenko University of KyivKyivUkraine
  2. 2.University of DebrecenDebrecenHungary

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