An Adaptive-Priority Queue

Abstract

Priority scheduling is used frequently in computer systems; however, such schedules usually have a “fail-safe” provision to prevent high-priority requests from causing unlimited delay to low-priority ones. In this paper, a queue and server is considered which has two sources of Poisson-arrival customers, types a and b respectively. Non-preemptive priority is granted to type a customers, except that whenever the number of waiting type b customers exceeds a specified threshold, class b receives priority. Service times are assumed exponentially distributed with a common mean, but it is possible to greatly relax this restriction. The intent is to grant priority to class a most of the time, while bounding the mean waiting time of class b customers under heavy class a load. This particular fail-safe mechanism is shown to have the property that for system states in which class b is below the threshold, the occupancy probability is exactly the same as if class a always had high priority.