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

Abstract

Motivated by the work of Whitt (Queueing Syst 81(4):341-378, 2015) andMa and Whitt (in: Winter simulation conference, pp 2598-2609, 2015), that studied performance stabilization in a GIt /GIt /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 GIt /GIt /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 GIt /GIt /1/ PS queue. Extensive simulation studies with various settings of arrival processes and service times show that the DMcontrol outperforms the SR control for heavy-traffic conditions, and that the SR control performs better for lighttraffic conditions.