Abstract：By the approaches of being linearly close to the workload of tasks in hard real-time system, the closer response time upper bound can be used to decrease the running time. At the same time, it is linear in time of complexity for the upper bound in the sufficient schedulable tests of task sets. In interactive system design tools, system optimization via search, and admission of new tasks into dynamic systems, this new linear upper bound can considerably improve the efficiency of test. Further, the scheduling model has wide application range because it does not have the limits of deadline and jitter. The pertinent experiments show that the method of utilizing the approximate upper time improves the efficiency of accurate test of the scheduling.