Approaches to analysis and simplification of non-Markovian system models

Abstract

In this thesis, we present an algorithm to transform a subset of generalized semi-Markov processes into semi-Markov processes. The transformation preserves steady-state simulation, a simulation that allows us to retrieve the steady state probability of the generalized semi-Markov process from that of the transformed process. The method presented could generate semi-Markov processes with big state spaces, for that reason we introduce a two state simplification techniques. The first one deals with the state space explosion problem by deleting states from the original generalized semi-Markov process. The aim of this technique is to generate semi-Markov processes with smaller state space. The technique deletes states from the generalized semi-Markov process while preserving the distribution of time needed to travel between non-deleted states; the technique also preserves the transient state probabilities of a subset of the states in the process. The other technique deals with the state space explosion problem at the level of semi-Markov processes. It works by deleting states from the semi-Markov processes while preserving the average time to travel between non-deleted states, or what we call mean passage-time equivalence, the technique also preserves the steady state probabilities of a subset of the states in the process.