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Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates

Author

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  • Yongkyu Cho

    (Samsung Electronics)

  • Young Myoung Ko

    (Pohang University of Science and Technology (POSTECH))

Abstract

Motivated by the work of Whitt (Queueing Syst 81(4):341–378, 2015) and Ma and Whitt (in: Winter simulation conference, pp 2598–2609, 2015), that studied performance stabilization in a $$GI_t/GI_t/1$$ G I t / G I t / 1 queue, this research study investigates the stabilization of the mean virtual response time in a single-server processor sharing (PS) queueing system with a time-varying arrival rate and a service rate control (a $$GI_t/GI_t/1/PS$$ G I t / G I t / 1 / P S queue). We propose and compare a modified square-root (SR) control and a difference-matching (DM) control to stabilize the mean virtual response time of a $$GI_t/GI_t/1/PS$$ G I t / G I t / 1 / P S queue. Extensive simulation studies with various settings of arrival processes and service times show that the DM control outperforms the SR control for heavy-traffic conditions, and that the SR control performs better for light-traffic conditions.

Suggested Citation

  • Yongkyu Cho & Young Myoung Ko, 2020. "Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates," Annals of Operations Research, Springer, vol. 293(1), pages 27-55, October.
    • Handle: RePEc:spr:annopr:v:293:y:2020:i:1:d:10.1007_s10479-019-03511-9
    DOI: 10.1007/s10479-019-03511-9
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    References listed on IDEAS

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