This letter analyzes quantum-based scheduling of real-time tasks when each task is allowed to have a different quantum size. It is shown that generalized quantum-based scheduling dominates preemption threshold scheduling in the sense that if tasks are schedulable by preemption threshold scheduling then the tasks must be schedulable by generalized quantum-based scheduling, but the converse does not hold. To determine the schedulability of tasks in quantum-based scheduling, a method to calculate the worst case response time is also presented.

It is known that the schedulability of a non-preemptive task set with fixed priority can be determined in pseudo-polynomial time. However, since Rate Monotonic scheduling is not optimal for non-preemptive scheduling, the applicability of existing polynomial time tests that provide sufficient schedulability conditions, such as Liu and Layland's bound, is limited. This letter proposes a new sufficient condition for non-preemptive fixed priority scheduling that can be used for any fixed priority assignment scheme. It is also shown that the proposed schedulability test has a tighter utilization bound than existing test methods.