Far Eastern Mathematical Journal

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Jackson network in a random environment: strong approximation


Elena Bashtova, Elena Lenena

2020, issue 2, Ñ. 144-149
DOI: https://doi.org/10.47910/FEMJ202015


Abstract
We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random variables. We establish a theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in positive orthant.

Keywords:
Jackson network, Strong approximation, Unreliable systems

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