RATE OF CONVERGENCE OF FLUID APPROXIMATION FOR RE-ENTRANT LINES UNDER FBFS DISCIPLINE

The re-entrant line networks under a first-buffer-first-served (FBFS) service discipline are considered in this paper. Under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid limit processes with an exponential rate, we prove that the scaled processes characterizing the re-entrant line converge to the corresponding fluid limit processes with the exponential rate. Here the scaled processes include the queue length process, workload process, busy time process and idle time process.