A GSPN Semantics for CTBN with Immediate Nodes

In this report we present an extension to Continuous Time Bayesian Networks (CTBN) called Generalized Continuous Time Bayesian Networks (GCTBN). The formalism allows one to model, in addition to continuous time delayed variables (with exponentially distributed transition rates), also non delayed or “immediate” variables, which act as standard chance nodes in a Bayesian Network. This allows the modeling of processes having both a continuous-time temporal component and an immediate (i.e. non-delayed) component capturing the logical/probabilistic interactions among the model’s variables. The usefulness of this kind of model is discussed through an example concerning the reliability of a simple component-based system. A semantic model of GCTBNs, based on the formalism of Generalized Stochastic Petri Nets (GSPN). is outlined, whose purpose is twofold: to provide a well-defined semantics forGCTBNs in terms of the underlying stochastic process, and to provide an actual mean to perform inference (both prediction and smoothing) on GCTBNs. The example case study is then used, in order to highlight the exploitation of GSPN analysis for posterior probability computation on the GCTBN model. Acronym list: BN Bayesian belief Network CIM Conditional Intensity Matrix CPT Conditional Probability Table CTBN Continuous Time Bayesian Network CTMC Continuous Time Markov Chain DBN Dynamic Bayesian Network FTA Fault Tree Analysis GCTBN Generalized Continuous Time Bayesian Network GSPN Generalized Stochastic Petri Net MRF Markov Random Field