Fallible Petri Nets and Markov Decision Processes
Stochastic Petri nets are Petri nets that have a stochastic process that is defined by the probabilistic firing delay of transitions. Because the transitions have a firing delay placed upon them, that requires the introduction of time into the semantics of a Petri net, which was implicitly a part of Petri nets when originally defined by Carl Petri. Fallible Petri nets are stochastic Petri nets that do not require time to be used but has the probabilistic process introduced by having transitions that can fail to fire even if enabled by use of random variables based on a Bernoulli distribution. Fallible Petri nets are then further explored by translating them into a Markov decision process and then a Markov chain.
Committee: Andrew Miner (major professor), Gianfranco Ciardo, and Samik Basu