Bayesian networks, influence diagrams, and games in simulation metamodeling

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Jirka Poropudas Name of the doctoral dissertation Bayesian Networks, Influence Diagrams, and Games in Simulation Metamodeling Publisher Aalto University Unit School of Science, Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 76/2011 Field of research Systems and operations research Manuscript submitted 16 August 2011 Manuscript revised 16 August 2011 Date of the defence 21 October 2011 Language English Monograph Article dissertation (summary + original articles) Abstract The Dissertation explores novel perspectives related to time and conflict in the context of simulation metamodeling referring to auxiliary models utilized in simulation studies. The techniques innovated in the Dissertation offer new analysis capabilities that are beyond the scope of the existing metamodeling approaches. In the time perspective, dynamic Bayesian networks (DBNs) allow the probabilistic representation of the time evolution of discrete event simulation by describing the probability distribution of the simulation state as a function of time. They enable effective what-if analysis where the state of the simulation at a given time instant is fixed and the conditional probability distributions related to other time instants are updated revealing the conditional time evolution. The utilization of influence diagrams (IDs) as simulation metamodels extends the use of the DBNs into simulation based decision making and optimization. They are used in the comparison of decision alternatives by studying their consequences represented by the conditional time evolution of the simulation. For additional analyses, random variables representing simulation inputs can be included in both the DBNs and the IDs. In the conflict perspective, the Dissertation introduces the game theoretic approach to simulation metamodeling. In this approach, existing metamodeling techniques are applied to the simulation analysis of game settings representing conflict situations where multiple decision makers pursue their own objectives. Game theoretic metamodels are constructed based on simulation data and used to study the interaction between the optimal decisions of the decision makers determining their best responses to each others' decisions and the equilibrium solutions of the game. Therefore, the game theoretic approach extends simulation based decision making and optimization into multilateral settings. In addition to the capabilities related to time and conflict, the techniques introduced in the Dissertation are applicable for most of the other goals of simulation metamodeling, such as validation of simulation models. The utilization of the new techniques is illustrated with examples considering simulation of air combat. However, they can also be applied to simulation studies conducted with any stochastic or discrete event simulation model.The Dissertation explores novel perspectives related to time and conflict in the context of simulation metamodeling referring to auxiliary models utilized in simulation studies. The techniques innovated in the Dissertation offer new analysis capabilities that are beyond the scope of the existing metamodeling approaches. In the time perspective, dynamic Bayesian networks (DBNs) allow the probabilistic representation of the time evolution of discrete event simulation by describing the probability distribution of the simulation state as a function of time. They enable effective what-if analysis where the state of the simulation at a given time instant is fixed and the conditional probability distributions related to other time instants are updated revealing the conditional time evolution. The utilization of influence diagrams (IDs) as simulation metamodels extends the use of the DBNs into simulation based decision making and optimization. They are used in the comparison of decision alternatives by studying their consequences represented by the conditional time evolution of the simulation. For additional analyses, random variables representing simulation inputs can be included in both the DBNs and the IDs. In the conflict perspective, the Dissertation introduces the game theoretic approach to simulation metamodeling. In this approach, existing metamodeling techniques are applied to the simulation analysis of game settings representing conflict situations where multiple decision makers pursue their own objectives. Game theoretic metamodels are constructed based on simulation data and used to study the interaction between the optimal decisions of the decision makers determining their best responses to each others' decisions and the equilibrium solutions of the game. Therefore, the game theoretic approach extends simulation based decision making and optimization into multilateral settings. In addition to the capabilities related to time and conflict, the techniques introduced in the Dissertation are applicable for most of the other goals of simulation metamodeling, such as validation of simulation models. The utilization of the new techniques is illustrated with examples considering simulation of air combat. However, they can also be applied to simulation studies conducted with any stochastic or discrete event simulation model.