Weak convergence for generalized semi-Markov processes

Interactive Generalized Semi-Markov Processes

We have previously introduced Generalized Semi-Markovian Process Algebra (GSMPA), a process algebra based on ST semantics which is capable of expressing durational actions, where durations are expressed by general probability distributions. In this paper we introduce the calculus of Interactive Generalized Semi-Markov Processes (IGSMP), a variant of GSMPA where synchronizable actions are restri...

Continuity of Generalized Semi-Markov Processes

It is shown that sequences of generalized semi-Markov processes converge in the sense of weak convergence of random functions if associated sequences of defining elements (initial distributions, transition functions and clock time distributions) converge. This continuity or stability is used to obtain information about invariant probability measures. It is shown that there exists an invariant p...

Numerical Analysis of Generalized Semi-Markov Processes

This paper present methodological results that allow the cost-effective numerical analysis of finite-state generalized semi-Markov processes (GSMPs) with exponential and deterministic events by an embedded general state space Markov chain (GSSMC). Key contributions constitute the formal proof that elements of the transition kernel of the GSSMC can always be computed by appropriate summation of ...

The KTH Visit in Semi-Markov Processes

Monte Carlo Simulation of Markov, Semi-Markov, and Generalized Semi- Markov Processes in Probabilistic Risk Assessment

Most probabilistic risk assessment (PRA) and reliability methods commonly used at Johnson Space Center (JSC) make the assumption that component failures in a system are independent random occurrences. There are some exceptions (e.g. modeling common cause events), but because of the mathematical complications that occur when full dependency is assumed, it is not done by the standard models. This...