Heavy Traac Gaussian Asymptotics of On-oo Uid Model On-oo Uid Models in Heavy Traac Environment

We consider uid models with innnite buuer size. Let fZ N (t)g be the net input rate to the buuer where fZ N (t)g is a superposition of N homogeneous alternating on-oo ows. Under heavy traac environment fZ N (t)g converges in distribution to a centered Gaussian process with covariance function of a single ow. The aim of this paper is to prove the convergence of the stationary buuer content process fX N (t)g in the N th model to the buuer content process fX (t)g in the limiting Gaussian model.