The Annals of Applied Probability

Control of the multiclass ${G/G/1}$ queue in the moderate deviation regime

Rami Atar and Anup Biswas

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Abstract

A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a differential game that can be explicitly solved. While the characterization of the limit by a differential game is akin to results at the large deviation scale, the analysis of the problem is closely related to the much studied area of control in heavy traffic at the diffusion scale.

Article information

Source
Ann. Appl. Probab., Volume 24, Number 5 (2014), 2033-2069.

Dates
First available in Project Euclid: 26 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1403812369

Digital Object Identifier
doi:10.1214/13-AAP971

Mathematical Reviews number (MathSciNet)
MR3226171

Zentralblatt MATH identifier
1306.60131

Subjects
Primary: 60F10: Large deviations 60K25: Queueing theory [See also 68M20, 90B22] 49N70: Differential games 93E20: Optimal stochastic control

Keywords
Risk-sensitive control large deviations moderate deviations differential games multi-class single-server queue heavy traffic

Citation

Atar, Rami; Biswas, Anup. Control of the multiclass ${G/G/1}$ queue in the moderate deviation regime. Ann. Appl. Probab. 24 (2014), no. 5, 2033--2069. doi:10.1214/13-AAP971. https://projecteuclid.org/euclid.aoap/1403812369


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References

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