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.