Probabilistic Models for the Execution Time in Stochastic Scheduling

Abstract: The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the objective. Despite being random variables, execution times are most often treated as deterministic in the literature, with few works taking advantage of their randomness; even in those, the underlying distributions are assumed as being normal or uniform for no particular reason. In this work we investigate these distributions in various machines and algorithms. A mathematical problem arises when dealing with samples whose populational minimum is unknown, so a significant portion of this monograph is dedicated to such problem. We propose several different effective or computationally cheap ways to overcome the problem, which also apply to execution times. These methods are tested experimentally, and results point to the superiority of our proposed inference methods. We demonstrate the existence of execution time distributions with long tails, and also conclude that two particular probability distributions were the most suitable for modelling all execution times. While we do not discuss direct applications to stochastic scheduling, we hope to promote the usage of probabilistic execution times to yield better results in, for example, task scheduling.