Analysis of hybrid Petri nets with random discrete events

More and more, our society and economy rely on the correct operation of, often hidden, critical infrastructures. These infrastructures such as the power grid and water and gas distribution networks, play an important role in our everyday life. Continuous supply of services from these assets is essential for people, organizations, and for the security and economy of our society. It is of substantial value to know or estimate how quickly such systems recover to acceptable levels of service after the occurrence of failures, natural disasters, e.g., fire, earthquakes, or cyber-attacks.\ud Critical infrastructure and naturally hybrid, i.e., one needs both discrete and continuous quantities to realistically describe their behaviour. More-over, in many modern applications there is an intrinsic uncertainty. This is particularly true for dependability analysis of critical infrastructures, where one must model the occurrence of failure and repair in a system.\ud In this dissertation we propose the use of an extended version of stochastic hybrid Petri nets. This modelling formalism combines discrete and continuous quantities with random discrete events. Furthermore, Petri nets provide a high level and easy-to-understand formalism. Particularly, we consider so called Hybrid Petri nets with General transitions (HPnG). The term general transition refers to the arbitrary nature of probability distribution that can be associated with stochastic variables in this model. HPnGs form a restricted subclass of stochastic hybrid models.\ud The arbitrary nature of random discrete events in HPnGs is the main challenge for their analysis. We tackle the analysis of HPnGs by a conditioning argument on the occurrence times of random discrete events. This idea leads to an efficient generation of the underlying state space, which provides us with a structure such that measures of interest can be computed exacly and effectively. Unfortunately, the exact computation of measures of interests for complex systems by HPnGs, will be shown to be inefficient. To overcome this, we will also investigate approximation techniques, providing upper and lower bounds for measures of interest. The approximation techniques are based on discretizing, the support of stochastic variables. Moreover, by smart generation and exploration of only parts of the state space, we can come up with upper and lower bounds for the given measures of interest. We will also investigate the feasibility of the methods introduced in this thesis, by considering two real-world applications, namely, dependability analysis of a sewage treatment facility, and a model of a smart house