In previous papers we developed a deterministic fluid approximation for anoverloaded Markovian queueing system having two customer classes and twoservice pools, known in the call-center literature as the X model. The systemuses the fixed-queue-ratio-with-thresholds (FQR-T) control, which we proposedin a recent paper as a way for one service system to help another in face of anunexpected overload. Under FQR-T, customers are served by their own servicepool until a threshold is exceeded. Then, one-way sharing is activated withcustomers from one class allowed to be served in both pools. The control aimsto keep the two queues at a pre-specified fixed ratio. We supported the fluidapproximation by establishing a many-server heavy-traffic functional weak lawof large numbers (FWLLN) involving an averaging principle. In this paper wedevelop a refined diffusion approximation for the same model based on amany-server heavy-traffic functional central limit theorem (FCLT).
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