Nonlinear Elastic Task Model and its Application to Adaptive Fair Sharing Control

In real-time systems, deadline misses of the tasks cause the degradation of qualities of their results. To improve the qualities, we have to allocate CPU utilization for each task adaptively. Recently, Buttazzo et al. address a feedback scheduling algorithm, which dynamically adjusts tasks' periods based on the current workloads by applying a linear elastic task model. In their model, the utilization allocated to each task is treated as the length of a linear spring and its flexibility is described by a constant elastic coefficient. In this paper, we first consider a nonlinear elastic task model, where the elastic coefficient depends on the utilization allocated to the task. We propose a simple iterative method for calculating the desired allocated resource and derive a sufficient condition for the convergence of the method. Next, we apply the nonlinear elastic model to an adaptive fair sharing controller. Finally, we show the effectiveness of the proposed method by computer simulation