A Class of Methods for Analyzing Stochastic Systems.

Abstract : This report summarizes the publications from our research on methods for analyzing stochastic systems. We studied three different system classes: (a) Probabilistic networks that model a variety of industrial and communications systems. These systems include data communications networks, voice communications networks, transportation networks, computer architectures, and electrical power systems. We corrected existing algorithms, derived the computational complexity of certain evaluations, and, based on new theoretical results, we proposed generalized algorithms that compute a performability measure by means of an iterative partition of the network state space. We also developed confidence intervals for Monte Carlo simulations tailored to the estimation of performability measures. (b) 'Intelligent' Markovian networks where the processing of the units at the nodes and the routing of the units depend dynamically on the network congestion, and units can move concurrently. (c) Highly dependable systems with repairs. We have identified problems with existing simulation methods for estimating dependability measures and we are currently developing new methods that appear to be successful in a variety of large systems.