关键词: 实时系统, 静态优先级, 先入先出（FIFO）, 优先级受限, 可调度性分析, 高利用率

Abstract: In the area of communication，radar，navigation and various electronic production，embedded real-time scheduling has became the control kernel of those electronic and electrical systems.In fixed priority systems where tasks with the same priority are queued in FIFO（First In First Out） order，counterexamples are used to point out that the necessary assertion of Katcher’s schedulability condition does not hold.A necessary and sufficient condition for fixed priority scheduling with limited priority levels is proposed and proved analytically.Stochastic analysis show that when the execution times of different tasks are remarkably distinct with each other，approximately 15% of schedulable task sets are misjudged by Katcher’s condition.Further simulations show that Liu’s condition，Lehoczky’s condition，and Bini’s condition cannot deal with tasks with the same priority，Katcher’s condition does not hold for its necessary assertion；meanwhile the condition provides the necessary and sufficient perspective of off-line schedulability checking.This method provides an off-line tool for top-down design of real-time scheduling with high utilization.

Key words: real-time system, Fixed Priority（FP）, First In First Out（FIFO）, limited priority level, schedulablity analysis, high utilization