Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates
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Motivated by the work of Whitt, who studied stabilization of the mean virtual waiting time (excluding service time) in a GI_t/GI_t/1/FCFS queue, this paper 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 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 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.
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