Symbolic analysis of stochastic discrete event systems
In this dissertation we focus on modeling and verification of stochastic discrete event systems using Generalized Semi-Markov Processes (GSMPs). This class of processes includes many other important classes such as semi-Markov Processes, continuous time Markov chains, certain subclasses of regenerative processes and others. It has a wide range of applications from classical problems in queuing theory to modern research on modeling of power-aware devices. We present algorithms for solving three verification problems. The first two are dealing with transient properties of GSMPs. They are "bounded until" and "unbounded until" reachability problems—knowing a distribution over the initial states of a process we are interested in the probability that the process will reach a destination state staying in safe locations only. In the bounded version of the problem we require an additional upper bound on the number of events that are needed to reach a destination. The third verification problem is to find the stationary distribution of a GSMP and compute related steady state properties. Compared to previously known analytical methods for probabilistic systems, our approach removes restrictions on the number of concurrently active events scheduled with non-exponential distributions and allows modeling with a wide class of distributions whose densities are given as sums of terms, such that every term is a product of polynomials and exponentials. Compared to the simulation techniques, our method is more efficient in detecting rare event probabilities, and it determines the exact probabilities. The unifying idea of our algorithms is an application of symbolic computational methods to the functions and expressions defined on the regions of GSMP state space partitions with a certain regular structure.
Bernadsky, Mikhail, "Symbolic analysis of stochastic discrete event systems" (2008). Dissertations available from ProQuest. AAI3309398.