On–off fluid models in heavy traffic environment

We consider fluid models with infinite buffer size. Let {ZN(t)} be the net input rate to the buffer, where {{ZN(t)} is a superposition of N homogeneous alternating on–off flows. Under heavy traffic environment {{ZN(t)} 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 {XN*(t)} in the fNth model to the buffer content process {XN(t)} in the limiting Gaussian model.

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