Jackson network in a random environment: strong approximation
arXiv:2010.14582
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.
Submitted to Far Eastern Mathematical Journal (Dal'nevostochnyi Matematicheskii Zhurnal)