On–off fluid models in heavy traffic environment

We consider fluid models with infinite buffer size. The net input rate to the buffer is a superposition of N homogeneous alternating on–off flows. Under heavy traffic environment, the net input rate converges in distribution to a centred Gaussian process with covariance function of a single flow. The aim of this paper is to prove the convergence of the stationary buffer content process in the Nth model to the buffer content process in the limiting Gaussian model.