Calculating probabilities of real-time test cases

When testing a system, it is often necessary to execute a suspicious trace in a realistic environment. Due to nondeterministic choices existing in concurrent systems, such a particular trace may not be scheduled for execution. Thus it is useful to compute the probability of executing the trace. Our probabilistic model of real-time systems requires that for each transition, the period from the time when its enabling condition becomes satisfied to the time when it is fired is bounded and the length of the period obeys a probabilistic distribution. This model is not Markovian if the distribution is not exponential. Therefore it cannot be analyzed by Markov processes. We propose to use integration to calculate the probability for a path. Then we discuss the possibility to optimize the calculation