Compositional modelling using Petri nets with the analysis power of stochastic hybrid processes

A general stochastic hybrid process (GSHP) is a mathematical formalism that covers most of the requirements posed by the modelling of complex operations, such as time dependencies, multi-dimensional continuous as well as discrete processes, discontinuities, randomness and model uncertainties. In addition, it is possible to study GSHP by using stochastic analysis methodologies, thereby empowering it with powerful mathematical properties. This guarantees unambiguous simulation possibility of the model and allows speeding up this simulation while keeping the model properties intact. However, using GSHP to construct a model of a complex operation is not easy. To support the modelling and the subsequent verification both by mathematical and by multiple operational domain experts, a supporting graphical modelling formalism is desired. Petri nets have shown to be useful for developing models of various complex applications. Typical Petri net features are concurrency and synchronisation mechanism, hierarchical and modular construction, and natural expression of causal dependencies, in combination with graphical and analytical representations.\ud \ud The aim of this thesis is to combine the strengths of Petri net modelling formalisms and those of GSHP. First, dynamically coloured Petri nets (DCPN) are developed, and proof of equivalence is provided with piecewise deterministic Markov processes, which is a particular class of GSHP. Next, DCPN are extended to stochastically and dynamically coloured Petri nets (SDCPN), and proof of equivalence is provided with GSHP. Subsequently, SDCPN are extended to SDCPN with interconnection mapping types (SDCPNimt) and proof of equivalence is provided with both SDCPN and GSHP. It is shown with illustrative air transport examples that these three classes of Petri net are very effective when it comes to the compositional modelling of operations consisting of many distributed components that behave and interact in a dynamic way with many uncertainties. With the equivalence relations between these formalisms, the properties and strengths of the various approaches are combined. The many applications of the approach developed in this thesis, executed at NLR and beyond, show that both the approach and its combined strengths are acknowledged and supported by practice