Decision process petri nets: Analysis and optimization

In this paper we introduce a new modeling paradigm for developing decision process representation called Decision Process Petri Nets (DPPN). It extends the place-transitions Petri net theoretic approach by including the Markov decision process. Place-transitions Petri nets (PN) are used for process representation taking advantage of the formal semantic and the graphical display. Markov decision processes is utilized as a tool for trajectory planning via an utility function. The main point of the DPPN is its ability to represent the mark-dynamic and trajectory-dynamic properties of a decision process. Within the mark-dynamic properties framework we show that the DPPN theoretic notions of equilibrium and stability are those of the place-transitions Petri net. In the trajectory-dynamic properties framework, we optimized the utility function used for trajectory planning in the DPPN via a Lyapunov like function, obtaining as a result new characterizations for final decision points (optimum point) and stability. Moreover, we show that the DPPN mark-dynamic and Lyapunov trajectory-dynamic properties of equilibrium, stability an final decision points (optimum point) converge under certain restrictions. We propose an algorithm for optimum trajectory planning, that makes use of the graphical representation of the place-transitions Petri net and the utility function. The paradigm is applied to one player's games, where some well known results are presented but from a different perspective. Business process modeling is also considered. This work makes firm steps toward the modelling and analysis of problems, in the fields of decision process systems and theory of games, using DPPN.