The proxel-based method: formalisation, analysis and applications [Elektronische Ressource] / von Sanja Lazarova-Molnar

The Proxel-Based Method:Formalisation, Analysis andApplicationsDissertationzur Erlangung des akademischen GradesDoktoringenieurin(Dr.-Ing.)angenommen durch der Fakultat fur Informatik¨ ¨der Otto-von-Guericke-Universita¨t MagdeburgvonDipl.-Ing. M. Sc. Sanja Lazarova-Molnargeboren am 26.Februar1977 in Skopje, MazedonienGutachter: Prof.Dr. Graham HortonDoz.Dr. Rudiger Hohmann¨Prof.Dr. Helena SzczerbickaMagdeburg, den 11. November 2005AbstractTheproxel-basedmethodisanintuitiveapproachtoanalysingdiscretestochasticmod-els, suchas are describedbystochastic Petrinets orqueuing systems forexample. Theapproach analyses models in a deterministic manner, avoiding the typical problemsof discrete-event simulation (e.g. finding good-quality pseudo-random-number genera-tor) and partial differential equations (difficult to set up and solve). The underlyingstochastic process is a discrete-time Markov chain which is constructed on-the-fly byinspecting all possible behaviours of the model. The proxel-based simulation is shownto be very useful in analysing some classes of reliability models and fault-trees. Inparticular it is more efficient than the discrete-event approach applied to the samemodels, because the proxel-based method is less sensitive to the stiffness of the mod-els.