Probabilistic Analysis of Multi-processor Scheduling of Tasks with Uncertain Parameters

Abstract

A new approach is proposed for the probabilistic assessment of schedulability of periodic tasks with uncertain characteristics in dynamic multi–processor scheduling. It is aimed at non–critical real–time applications such as multimedia, which allow some leeway with respect to compliance with timing requirements, provided that certain minimum Quality of Service (QoS) requirements are met. Uncertainties are taken into account through random variables at the task arrival times and by characterising subsequent task characteristics in probabilistic terms. By examining each pair of possible computation time and deadline of a given task at each time unit in relation to the same of other tasks, an execution pattern is derived. This forms the basis for computing various QoS attributes such as probability of successful execution, latency in response time, jitter, etc. Illustrative examples address, amongst others, the performance of two particular algorithms, EDF and LLF, in the presence of uncertainties in task characteristics.