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Queueing Systems
Published in: Queueing Systems 4/2014

01-04-2014

Diffusion approximation for an overloaded X model via a stochastic averaging principle

Authors: Ohad Perry, Ward Whitt

Published in: Queueing Systems | Issue 4/2014

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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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Metadata
Title
Diffusion approximation for an overloaded X model via a stochastic averaging principle
Authors
Ohad Perry
Ward Whitt
Publication date
01-04-2014
Publisher
Springer US
Published in
Queueing Systems / Issue 4/2014
Print ISSN: 0257-0130
Electronic ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-013-9363-9

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