Jackson network in a random environment: strong approximation
Probability
2020-10-29 v1
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
Cite
@article{arxiv.2010.14582,
title = {Jackson network in a random environment: strong approximation},
author = {Elena Bashtova and Elena Lenena},
journal= {arXiv preprint arXiv:2010.14582},
year = {2020}
}
Comments
Submitted to Far Eastern Mathematical Journal (Dal'nevostochnyi Matematicheskii Zhurnal)