Design and Identification of Stochastic and Deterministic Stochastic Petri Nets

In this paper, we consider the identification problem of stochastic and deterministic stochastic Petri nets (PNs). The approach herein proposed consists of inferring a PN structure and identifying its parameters. Hence, the first step leads to the synthesis of a PN structure with the measurable sequence of events and states. This approach determines the measurable part and estimates the nonmeasurable part of the PN to be established. Once both parts are obtained, the PN structure and the initial marking of the nonmeasurable places are obtained thanks to the integer linear programming technique. In the second step of this approach, the parameters of the obtained model are estimated. Stochastic and deterministic stochastic PNs with deterministic and exponentially distributed transition durations are considered. A systematic identification method is proposed based on event sequences that are recorded by supervision systems. This method is based on a Markov model whose state space is isomorphic to the reachability graph of the untimed PN model.