Time-dependent Priority Disciplines: A Heavy Traffic Analysis

In this work, we revisit the theory underlying a range of time-dependent priority disciplines, and extend it to include the requirements of a class of applications that has not been studied in the past. Specifically, we target applications and services in which a scarce resource, or a fraction thereof, has to be awarded to a large number of concurrent requests. We thus consider an heavy traffic regime, and derive closed form expressions to evaluate the relative difference – in terms of average waiting times – of requests that belong to different priority classes. Our analysis allows to derive the expected waiting time of requests in single server queueing systems, under the assumption of finite buffers for both non-preemptive and preemptive cases. Additionally, we extend our results to a distributed scenario composed of an interconnected set of a large number of unreliable single server queueing systems. We then describe a number of applications and illustrate how to use our theoretic foundation to analyze and tune their performance. The accuracy of our analysis is validated through a set of experiments that we performed in a synthetic setting. Index Terms Dynamic Priority, Finite Buffer, Closed Systems, Fundamental Results