Jackson network in a random environment: strong approximation

Elena Bashtova; Elena Lenena

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arXiv · 2010.14582

Jackson network in a random environment: strong approximation

Elena Bashtova·Elena Lenena

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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.

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Elena Bashtova, Elena Lenena. 2020-10-27. Jackson network in a random environment: strong approximation. https://arxiv.org/abs/2010.14582

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