Schedulability analysis of applications with stochastic task execution times

Abstract

In the past decade, the limitations of models considering fixed (worst-case) task execution times have been acknowledged for large application classes within soft real-time systems. A more realistic model considers the tasks having varying execution times with given probability distributions. Considering such a model with specified task execution time probability distribution functions, an important performance indicator of the system is the expected deadline miss ratio of the tasks and of the task graphs. This article presents an approach for obtaining this indicator in an analytic way. Our goal is to keep the analysis cost low, in terms of required analysis time and memory, while considering as general classes of target application models as possible. The following main assumptions have been made on the applications that are modeled as sets of task graphs: the tasks are periodic, the task execution times have given generalized probability distribution functions, the task execution deadlines are given and arbitrary, the scheduling policy can belong to practically any class of non-preemptive scheduling policies, and a designer supplied maximum number of concurrent instantiations of the same task graph is tolerated in the system. Experiments show the efficiency of the proposed technique for monoprocessor systems.