Diffusion Approximation for an Overloaded X Model Via a Stochastic Averaging Principle
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 in a recent paper 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 many-server heavy-traffic functional weak law of large numbers (FWLLN) involving an 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 (FCLT).
Cite
@article{arxiv.1008.1729,
title = {Diffusion Approximation for an Overloaded X Model Via a Stochastic Averaging Principle},
author = {Ohad Perry and Ward Whitt},
journal= {arXiv preprint arXiv:1008.1729},
year = {2013}
}