Diffusion approximation for an overloaded X model via a stochastic averaging principle |
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Authors: | Ohad Perry Ward Whitt |
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Institution: | 1. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 60208, USA 2. Department of Industrial Engineering and Operations Research, Columbia University, New York, NY, 10027-6699, USA
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Abstract: | In previous papers we developed a deterministic fluid approximation for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the fixed-queue-ratio-with-thresholds (FQR-T) control, which we proposed as a way for one service system to help another in face of an unexpected overload. Under FQR-T, customers are served by their own service pool until a threshold is exceeded. Then, one-way sharing is activated with customers from one class allowed to be served in both pools. The control aims to keep the two queues at a pre-specified fixed ratio. We supported the fluid approximation by establishing a functional weak law of large numbers involving a stochastic averaging principle. In this paper we develop a refined diffusion approximation for the same model based on a many-server heavy-traffic functional central limit theorem. |
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