Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline

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 [21] in estimating the performance measures of the re-entrant lines with a FBFS discipline.Supported in part by a grant from NSERC (Canada).Supported in part by a grant from NSERC (Canada); the research was done while the author was visiting the Faculty of Commerce and Business Administration, UBC, Canada.