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# Theory of Probability and Mathematical Statistics (Teoriya Imovirnostei ta Matematychna Statystyka)

## On asymptotic merging of nodes' set in stochastic networks

### E. A. Lebedev, H. V. Livinska

Abstract: For multichannel stochastic networks the problem of asymptotic merging of the queueing nodes' set is considered. Under heavy traffic conditions in the network, a functional limit theorem for a multidimensional service process is proved. The statement of the theorem concerns to the convergence of the service process to a Gaussian diffusion process. Under the asymptotic merging condition, the dimension of the approximating process is reduced, and its characteristics can be written via network parameters in explicit form.

Keywords:

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