2010/08/10 by Ohad Perry, Ward Whitt, Perry, Ohad +1
Business, Management and Accounting · Social Sciences · Decision Sciences · #Advanced Queuing Theory Analysis #Transportation Planning and Optimization #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.1008.1729
In previous papers we developed a deterministic fluid approximation for an\noverloaded Markovian queueing system having two customer classes and two\nservice pools, known in the call-center literature as the X model. The system\nuses the fixed-queue-ratio-with-thresholds (FQR-T) control, which we proposed\nin a recent paper as a way for one service system to help another in face of an\nunexpected overload. Under FQR-T, customers are served by their own service\npool until a threshold is exceeded. Then, one-way sharing is activated with\ncustomers from one class allowed to be served in both pools. The control aims\nto keep the two queues at a pre-specified fixed ratio. We supported the fluid\napproximation by establishing a many-server heavy-traffic functional weak law\nof large numbers (FWLLN) involving an averaging principle. In this paper we\ndevelop a refined diffusion approximation for the same model based on a\nmany-server heavy-traffic functional central limit theorem (FCLT).\n