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Asymptotically optimal control of N-systems with $$H_2^*$$ H 2 ∗ service times under many-server heavy traffic

Author

Listed:
  • Arka Ghosh

    (Iowa State University)

  • Keguo Huang

    (Iowa State University)

Abstract

We address a control problem for a queueing system, known as the “N-system,” under the Halfin–Whitt heavy-traffic regime. It has two customer classes and two server pools: servers from one pool can serve both customer classes, while servers from the other pool can only serve one class. The service time is assumed to follow a special case of hyper-exponential distributions, called the $$H^*_2$$ H 2 ∗ distribution, and customers are impatient. We consider an expected infinite-horizon discounted cost function, with linear holding and abandonment cost components. A static priority policy is proposed and is shown to be asymptotically optimal in a certain parameter regime, using weak convergence techniques.

Suggested Citation

  • Arka Ghosh & Keguo Huang, 2017. "Asymptotically optimal control of N-systems with $$H_2^*$$ H 2 ∗ service times under many-server heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 35-60, June.
    • Handle: RePEc:spr:queues:v:86:y:2017:i:1:d:10.1007_s11134-017-9518-1
    DOI: 10.1007/s11134-017-9518-1
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    References listed on IDEAS

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    1. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    2. J. G. Dai & Tolga Tezcan, 2011. "State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 271-320, May.
    3. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    4. Tolga Tezcan & J. G. Dai, 2010. "Dynamic Control of N -Systems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic," Operations Research, INFORMS, vol. 58(1), pages 94-110, February.
    5. Ward Whitt, 2005. "Heavy-Traffic Limits for the G / H 2 */ n / m Queue," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 1-27, February.
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