Energy-Efficient Stochastic Task Scheduling on Heterogeneous Computing Systems

In the past few years, with the rapid development of heterogeneous computing systems (HCS), the issue of energy consumption has attracted a great deal of attention. How to reduce energy consumption is currently a critical issue in designing HCS. In response to this challenge, many energy-aware scheduling algorithms have been developed primarily using the dynamic voltage-frequency scaling (DVFS) capability which has been incorporated into recent commodity processors. However, these techniques are unsatisfactory in minimizing both schedule length and energy consumption. Furthermore, most algorithms schedule tasks according to their average-case execution times and do not consider task execution times with probability distributions in the real-world. In realizing this, we study the problem of scheduling a bag-of-tasks (BoT) application, made of a collection of independent stochastic tasks with normal distributions of task execution times, on a heterogeneous platform with deadline and energy consumption budget constraints. We build execution time and energy consumption models for stochastic tasks on a single processor. We derive the expected value and variance of schedule length on HCS by Clark's equations. We formulate our stochastic task scheduling problem as a linear programming problem, in which we maximize the weighted probability of combined schedule length and energy consumption metric under deadline and energy consumption budget constraints. We propose a heuristic energy-aware stochastic task scheduling algorithm called ESTS to solve this problem. Our algorithm can achieve high scheduling performance for BoT applications with low time complexity O(n(M+log n), where n is the number of tasks and M is the total number of processor frequencies. Our extensive simulations for performance evaluation based on randomly generated stochastic applications and real-world applications clearly demonstrate that our proposed heuristic algorithm can improve the weighted probability that both the deadline and the energy consumption budget constraints can be met, and has the capability of balancing between schedule length and energy consumption.