We consider a Jackson network in a general heavy traffic diffusion regime with the $\alpha$-parametrization. We also assume that each customer may abandon the system while waiting. We show that in this regime the queue-length process converges to a multi-dimensional regulated Ornstein–Uhlenbeck process.
"A Jackson network under general regime." Braz. J. Probab. Stat. 33 (3) 532 - 548, August 2019. https://doi.org/10.1214/18-BJPS401