New methods for quantitative evaluation of Markov regenerative models

The thesis describes the research that has been carried out in order to reduce the limitations of current analysis techniques for non-Markovian models, which led to a three-fold contribution. The first contribution is a technique that allows to integrate different analysis techniques for the evaluation of kernels of a MRGP. Specifically, the state space of the underlying timed model is analyzed to identify epochs between regenerations and apply distinct methods for their analysis depending on the locally satisfied conditions. For epochs not amenable to existing methods, an adaptive approximation of kernel entries based on partial exploration of the state space is proposed, leveraging heuristics that permit to reduce the error on transient probabilities. This approach extends the class of models that can be analyzed, reduces errors committed by approximate analysis and allows one to automatize the selection of the analysis technique. The second contribution is a technique for the computations of the equilibrium probability density functions (PDFs) for the continuous component of the state in MRGP. Equilibrium PDFs are derived as closed-form analytical expressions by applying the Key Renewal Theorem to stochastic state classes computed between regenerations. This techniques provides a basis to analyze system properties from the equilibrium such as survivability. The last contribution, is an extension of the analysis of hierarchical semi-Markov processes with parallel regions, a technique that evaluates steady-state probabilities of models with multiple concurrent non-Markovian timers in a compositional way without the need of full state space generation. Specifically, the technique has been extended by removing some of its limitations and increasing its modeling power. By applying the time advancement mechanism known from stochastic state classes, exits in parallel regions with different time origins can be taken into account. Furthermore, exits can be put on state borders such that the model evolution depends on the exited region and a concept for history states is also presented. This significantly increases modeling power, such that the gap between semi-Markov processes with restricted modeling power and non-Markovian models without modeling restrictions but also with less efficient analysis is filled.