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. ^
"Symbolic analysis of stochastic discrete event systems"
(January 1, 2008).
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