Abstract: In this paper we research the aperiodic soft real-time system in which the arrival time and the execution time of tasks are uncertain.According to the queuing theory,a aperiodic soft real-time system is a typical stochastic discrete event dynamic system and is usually considered as an M/M/1/H mixed queuing system.After a discussion of three performance metrics including rejection ratio,deadline miss ratio,and average deadline excess amount,we propose a design method for optimal buffer capacity based on these metrics.Lastly,the performance analysis shows that our method can improve the system's performance.