Supplement of “ Improvement of Real - Time Multi - Core Schedulability with Forced Non - Preemption ”

The technique in [4] uses the notion of interference [27]. The interference to τk in an interval of [a, b) (denoted by Ik(a, b)) represents the cumulative length of all intervals in [a, b) such that a job of τk is ready to execute but cannot be executed due to the execution of other ready jobs. Also, the interference of a task τi to another task τk in an interval of [a, b) (denoted by Ik←i(a, b)) represents the cumulative length of all intervals in [a, b) such that a job of τi executes but a job of τk cannot, although it is ready for execution. Since a job of τk does not execute in a given time slot only when m other jobs execute, the following equation holds under any global workconserving algorithm [27]: