Superposition properties and performance bounds of stochastic timed-event graphs

This paper addresses the performance evaluation of stochastic timed-event graphs. The transition firing times are random variables with general distribution. We first consider a stochastic timed-event graph in which the firing times are generated by time superposition (or addition) of two sets of random variable sequences. Properties of this system are established. Chiefly, we prove that the average cycle time is subadditive, i.e., it is smaller than the sum of the average cycle times of the two stochastic timed-event graphs in which the firing times are generated by one of the two sets of random variable sequences, respectively. Based on these superposition properties, we derive various upper bounds of the average cycle time of a general stochastic timed-event graph. In particular, we obtain upper bounds which converge to the exact average cycle time as the standard deviations of the firing times decrease. Finally, we derive performance bounds for stochastic timed-event graphs with bounded firing times