@phdthesis{Rohr2016, author = {Rohr, Christian}, title = {Simulative analysis of coloured extended stochastic Petri nets}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-41476}, school = {BTU Cottbus - Senftenberg}, year = {2016}, abstract = {Stochastic modelling of biochemical reaction networks is getting more and more popular. Throughout the past decades typical biological models increased in their size and complexity, because of advances in systems and molecular biology, in particular through the high-throughput omic technologies. Here biochemical networks of different levels of detail are modelled, starting with simple chemical reactions and signal transduction networks, up to individual cells and entire organisms. This increases the demand for efficient analysis methods. A Petri net is a mathematical modelling language for the description of concurrent behaviour of distributed systems. Its advantage is the ease of scalability of the models, which relates to the network's state space, as well as the structure of the network itself. In this work, we recall several stochastic simulation algorithms, e.g., exact as well as approximate methods. Furthermore, we introduce an approach to improve the efficiency of stochastic simulation for large and dense networks by a new approximate stochastic simulation algorithm called discrete-time leap method. We depict the wide range of simulative analyses of complex stochastic systems ranging from trace generation to the computation of transient solutions and steady state distributions. We set forth advanced analysis of stochastic models by means of simulative model checking. For the use of simulative model checking, we integrate the continuous stochastic (reward) logic (CS(R)L) and the probabilistic linear-time temporal logic with constraints (PLTLc). Simulative model checking has some limitations compared to the numerical methods, e.g., in principle it is possible to consider nested probabilistic formulas in CS(R)L, but not practical, since the calculation is not feasible in a reasonable period of time. In addition to the transient analysis, the steady state analysis is often of interest; therefore we have implemented two on-the-fly steady state detection methods. The first one is based on a "sample batch means" algorithm and is used in the linear-time temporal logic. The second approximates the steady state distribution and checks for convergence. We apply the aforementioned techniques to several case studies from systems biology and technical systems. The main contributions of this thesis to scientific knowledge are the development of the discrete-time leap method for the simulation of stochastic models, the approximations of transient solutions and steady state distributions by use of stochastic simulation for stochastic models and Markov reward models, the development of an infinite time horizon model checking algorithm exploiting the steady state property for PLTLc and CSL, and the first simulative model checking algorithm for CSRL incorporating state and impulse rewards. All presented algorithms and methods are implemented in the advanced analysis tool MARCIE.}, subject = {Coloured extended Stochastic Petri Nets; Stochastic simulation; Delta-leaping; Simulative model checking; Gef{\"a}rbte erweiterte stochastische Petri Netze; Stochastische Simulation; Delta-leaping; Simulatives Modelchecking; Stochastisches Modell; Gef{\"a}rbtes Petri-Netz; Model Checking}, language = {en} }