Threshold-based interventions to optimize performance in preemptive priority queues

This paper studies a single-server priority queueing model in which preemptions are allowed during the early stages of service. Once enough service effort has been rendered, however, further preemptions are blocked. The threshold where the change occurs is either a proportion of the service requirement, or time-based. The Laplace–Stieltjes transform and mean of each class sojourn time are derived for a model which employs this hybrid preemption policy. Both preemptive resume and preemptive repeat service disciplines are considered. Numerical examples show that it is frequently the case that a good combination of preemptible and nonpreemptible service performs better than both the standard preemptive and nonpreemptive queues. In a number of these cases, the thresholds that optimize performance measures such as overall average sojourn time are determined.