Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline
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The diffusion approximation is proved for a class of queueing networks, known as re-entrant lines, under a first-buffer-first-served (FBFS) service discipline. The diffusion limit for the workload process is a semi-martingale reflecting Brownian motion on a nonnegative orthant. This approximation has recently been used by Dai, Yeh and Zhou  in estimating the performance measures of the re-entrant lines with a FBFS discipline.
KeywordsRe-entrant lines diffusion approximation multiclass queueing network heavy traffic semi-martingale reflecting Brownian motion
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