On June 11th, 2010, Mariken Everdij of the NLR Air Transport Safety Institute successfully defended her PhD thesis for the University of Twente, The Netherlands. The graduation committee consisted of two supervisors, from the University of Twente and from the Embedded Systems Institute in Eindhoven, as well as seven leading experts in Stochastic Systems and Petri nets from the National Aerospace Laboratory NLR and from the Universities of Twente, Gent, Eindhoven and Groningen.
From left to right: Antoinette ten Veen (registrar), Aniek van der Valk (‘paranimf’), Mariken Everdij, Carolynne Montijn (‘paranimf’)
The title of Mariken’s thesis is “Compositional modelling using Petri nets with the analysis power of stochastic hybrid processes”. The thesis develops three classes of Petri net that can be used to model complex stochastic dynamic operations, such as those occurring in air transport. The Petri nets have rich building blocks that capture a large range of properties in a graphical format, such as continuous processes (e.g. position and velocity of an aircraft through time), uncertainties (such as wind or hazardous events), dynamics and variability (such as variation in reaction times of air traffic controllers), and discontinuities (such as changes in flight dynamics, from level flight to descent). In addition, the formalism has powerful tools to compose large Petri nets from interacting smaller nets. At the same time, the thesis shows that the Petri net classes developed are mathematically equivalent to a powerful class of stochastic hybrid process. The implication is that the analysis of these complex models can be made much more efficient, due to features such as temporarily pausing the analysis, and proceeding in more detail with the situations that are most safety-critical.
The Petri net classes developed in the thesis have already been successfully used many times, at NLR and beyond, to model a range of future and current air transport operations, for clients such as LVNL, Eurocontrol, and the European Commission. The models and the analysis tools have been used to determine the weak points and safety-critical issues for improvement of the operational concepts.
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