Discrete Frequency Selection of Frame-Based Stochastic Real-Time Tasks

Abstract

Energy-efficient real-time task scheduling has been actively explored in the past decade. Different from the past work, this paper considers schedulability conditions for stochastic real-time tasks. A schedulability condition is first presented for frame-based stochastic real-time tasks, and several algorithms are also examined to check the schedulability of a given strategy. An approach is then proposed based on the schedulability condition to adapt a continuous-speed-based method to a discrete-speed system. The approach is able to stay as close as possible to the continuous-speed-based method, but still guaranteeing the schedulability. It is shown by simulations that the energy saving can be more than 20% for some system configurations.

Energy-Aware Task Scheduling for Real-Time Systems with Discrete Frequencies

“…Formula (19) shows that the number of points in E 1 is exponential to the number of tasks and polynomial to the number of discrete frequencies and the number of bins of the tasks. The number of points in S 1 , which reflects the space needed to store the assistance data for scheduling, equals E 1 .…”

“…However, formula (19) has exposed that the number of line segments in the functions may suffer exponential growth, so does the time expense. This section presents an approximate method which brings out an algorithm with polynomial time complexity and maintains controllable error compared with the optimal expected energy consumption.…”

“…Xian and Lu [17] and Xu et al [15] deal with this problem by applying the research result from Ishihara and Yasuura [21] which uses two adjacent frequencies to execute task. Berten et al [19] also present a technique to adapt a continuous-speed-based method to a discrete-speed system. However, the derived solution is shown to be not optimal by Chen [18].…”

Managing Imprecise Worst Case Execution Times on DVFS Platforms

“…Vertical axis is the number of cycles, horizontal axis is the frame id, or the time. Figure 3 Second scenario (DIV workload): we consider nine tasks (we only present four of them here), using a number of cycles observed in an experimental environment (see [2]). Notice that at low loads, the number of killed jobs is usually very small, then the fairness is computed on a small number of jobs, which gives pretty much erratic values.…”

“…The same authors have also proposed a strategy taking the number of available speeds into account from the beginning, instead of patching algorithms developed for continuous speed processors [11]. In [2], we generalize and uniformize the model presented in several of the previous papers, and propose two contributions: first, we gave a general sufficient and necessary condition of schedulability for this model, and second, we presented a new approach to adapt a continuous-speedbased method to a discrete-speed system. Some multipro-cessor extensions have been considered in [4].…”