Probabilistic performance guarantee for real-time tasks with varying computation times

This paper describes how the scheduling algorithms and schedulability analysis methods developed for periodic tasks can be extended to provide performance guarantees to semi-periodic tasks. Like periodic tasks, the requests in a semi-periodic task are released regularly. However, their computation times vary widely. We focus on systems where the total maximum utilization of the tasks on each processor is larger than one. Hence according to the existing schedulability conditions for periodic tasks, we cannot guarantee that the semi-periodic tasks are schedulable, even though their total average utilization is very small. We describe two methods of providing probabilistic schedulability guarantees to the semi-periodic tasks: The first method, called probabilistic time-demand analysis, is a modification of the exact schedulability test for periodic tasks. The second method, called the transform-task method, transforms each task into a periodic task followed by a sporadic task. The transform-task method can provide an absolute guarantee to requests with shorter computation times and a probabilistic guarantee to the longer requests.