Probabilistic timing analysis of asynchronous systems with moments of delays

Finding time separation of events is a fundamental problem in the analysis of asynchronous systems. When component delays have statistical variations, it is both interesting and useful to compute moments of time separation of events. Traditionally, Monte Carlo simulation has been used for this purpose. However Monte Carlo simulation requires knowledge of the probability distributions of component delays, which is often difficult to ascertain. Much more easily available are parameters like the statistical mean and variance of component delays. Unfortunately, with only these parameters, Monte Carlo simulation cannot be reliably applied. Yet another disadvantage of Monte Carlo simulation is the large number of runs needed before the error term becomes small enough to be acceptable. This paper describes a polynomial-time algorithm for computing bounds on the first two moments of times of occurrence of events in an acyclic timing constraint graph, given only means and variances of component delays. We present experimental results demonstrating the effectiveness of our algorithm.