NEW ALGORITHM FOR SCHEDULING PERIODIC, REAL-TIME TASKS.

We consider the problem of preemptively scheduling a set of periodic, real-time tasks on a multiprocessor computer system. We give a new scheduling algorithm, and so-called Slack-Time Algorithm, and show that it is more effective than the known Deadline Algorithm. We also give an (exponential-time) algorithm to decide if a task system is schedulable by the Slack-Time or the Deadline Algorithm. The same algorithm can also be used to decide if a task system is schedulable by any given fixed-priority scheduling algorithm. This resolves an open question posed by Leung and Whitehead. Finally, it is shown that the problem of deciding if a task system is schedulable by the Slack-Time, the Deadline, or any given fixed-priority scheduling algorithm is NP-hard for each fixed m greater than equivalent to 1.