Nowadays the modelling and analysis of systems gain a more and more important role during the system design process. Petri nets and their extensions are one of the frequently used and popular modelling formalisms which provide efficient methods for modelling and analyzing distributed, asynchronous, parallel, concurrent and/or stochastic systems. Deriving the quantitative characteristics of a stochastic system is most often based on performing some kind of analysis on the Markovian model of the system.
The greatest problem with component based asynchronous systems is that the collective state space of components (i.e. the state space of the whole system) can be enormous. This is known as the state space explosion problem. Many times the huge size of the state space makes the stochastic analysis really hard or simply impossible. The conventional solution to this problem is to decompose the model, split it into smaller parts so it’s not necessary to store the complete state space of the system.
The state space explosion problem is present at two critical points during Markovian analyses: on one hand when storing the state space required by the algorithms, on the other hand storing the results of the analysis. In my thesis I examine and implement some efficient algorithms for handling the size of the state space, furthermore I recommend some changes in order to make the analyses even more efficient.