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 distributions. We first consider a stochastic timed event graph in which the transition firing times are generated by the superposition (or addition) of two sets of random variables. Properties of this system are established. Especially, we prove that the average cycle time is sub-additive, i.e. it is smaller than the sum of the average cycle times of the two stochastic timed event graphs obtained by assigning to each transition one of the two related random variables. Based on these superposition properties, we derive various upper bounds of the average cycle time of a general stochastic timed event graph. Especially, we obtain upper bounds which converge to the exact average cycle time as the standard deviations decrease. Finally, we derive performance bounds for stochastic timed event graphs with bounded transition firing times