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February 2014 Many-server heavy-traffic limit for queues with time-varying parameters
Yunan Liu, Ward Whitt
Ann. Appl. Probab. 24(1): 378-421 (February 2014). DOI: 10.1214/13-AAP927

Abstract

A many-server heavy-traffic FCLT is proved for the $G_{t}/M/s_{t}+\mathit{GI} $ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment according to a general probability distribution. The FCLT provides theoretical support for the approximating deterministic fluid model the authors analyzed in a previous paper and a refined Gaussian process approximation, using variance formulas given here. The model is assumed to alternate between underloaded and overloaded intervals, with critical loading only at the isolated switching points. The proof is based on a recursive analysis of the system over these successive intervals, drawing heavily on previous results for infinite-server models. The FCLT requires careful treatment of the initial conditions for each interval.

Citation

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Yunan Liu. Ward Whitt. "Many-server heavy-traffic limit for queues with time-varying parameters." Ann. Appl. Probab. 24 (1) 378 - 421, February 2014. https://doi.org/10.1214/13-AAP927

Information

Published: February 2014
First available in Project Euclid: 9 January 2014

zbMATH: 1290.60092
MathSciNet: MR3161651
Digital Object Identifier: 10.1214/13-AAP927

Subjects:
Primary: 60K25
Secondary: 60F17 , 90B22

Keywords: customer abandonment , deterministic fluid approximation , functional central limit theorem , Gaussian approximation , heavy traffic , Many-server queues , nonexponential patience distribution , nonstationary queues , queues with time-varying arrivals

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 2014
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