Jackson network in a random environment: strong approximation

Elena Bashtova, Elena Lenena

Published 2020-10-27Version 1

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.