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Optimality of the generalized $$\varvec{c\mu }$$ c μ rule in the moderate deviation regime

Author

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  • Rami Atar

    (Technion – Israel Institute of Technology)

  • Subhamay Saha

    (Indian Institute of Technology Guwahati)

Abstract

This paper studies a multiclass queueing system with an associated risk-sensitive cost observed in heavy traffic at the moderate deviation scale, accounting for convex queue length penalties. The main result is the asymptotic optimality of a dynamic index policy known from the diffusion-scale heavy traffic literature as the generalized $$c\mu $$ c μ rule.

Suggested Citation

  • Rami Atar & Subhamay Saha, 2017. "Optimality of the generalized $$\varvec{c\mu }$$ c μ rule in the moderate deviation regime," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 113-130, October.
    • Handle: RePEc:spr:queues:v:87:y:2017:i:1:d:10.1007_s11134-017-9523-4
    DOI: 10.1007/s11134-017-9523-4
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    References listed on IDEAS

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    1. Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
    2. Rami Atar & Asaf Cohen, 2016. "A Differential Game for a Multiclass Queueing Model in the Moderate-Deviation Heavy-Traffic Regime," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1354-1380, November.
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    Cited by:

    1. Asaf Cohen, 2019. "Brownian Control Problems for a Multiclass M/M/1 Queueing Problem with Model Uncertainty," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 739-766, May.
    2. Cohen, Asaf & Saha, Subhamay, 2021. "Asymptotic optimality of the generalized cμ rule under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 206-236.

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