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

Yongkyu Cho () and Young Myoung Ko ()
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Yongkyu Cho: Samsung Electronics
Young Myoung Ko: Pohang University of Science and Technology (POSTECH)

Annals of Operations Research, 2020, vol. 293, issue 1, No 3, 27-55

Abstract: 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.

Keywords: Stabilizing performance; Nonstationary queues; Processor sharing; Service rate control; Queueing simulation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-019-03511-9

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