Abstract
We consider fluid models with infinite buffer size. Let {Z N (t)} be the net input rate to the buffer, where {{Z N (t)} is a superposition of N homogeneous alternating on–off flows. Under heavy traffic environment {{Z N (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 {X * N (t)} in the fNth model to the buffer content process {X N (t)} in the limiting Gaussian model.
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Dębicki, K., Palmowski, Z. On–off fluid models in heavy traffic environment. Queueing Systems 33, 327–338 (1999). https://doi.org/10.1023/A:1019136415112
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DOI: https://doi.org/10.1023/A:1019136415112