Diffusion approximations for open queueing networks with service interruptions

This paper establishes functional central limit theorems describing the heavy-traffic behavior of open single-class queueing networks with service interruptions. In particular, each station has a single server which is alternatively up and down. There are two treatments of the up and down times. The first treatment corresponds to fixed up and down times and leads to a reflected Brownian motion, just as when there are no service interruptions, but with different parameters. To represent long rate interruptions, the second treatment has growing up and down times with the up and down times being of order n and n¹’/², respectively, when the traffic intensities are of order 1-n’-¹’/². In this case the authors establish convergence in the Skorohod M1 topology to a multidimensional reflection of multidimensional Brownian motion plus a multidimensional jump process.