A Probabilistic Extension of UML-B

keywords: UML-B, Event-B, probabilistic systems, interval probabilities, stochastic delay, probabilistic model verification, MDP, PRISM
This paper extends the graphical and formal language of UML-B to provide the ability to model probabilities. Discrete probabilities, interval probabilities, and stochastic delays are added to the UML-B's state-machine syntax, and their corresponding semantics are defined in Event-B. In addition, as a secondary contribution, UML-B (probabilistic) state-machine models are defined as MDP (Markov Decision Process) models in order to provide a means of quantitative verification in PRISM (Probabilistic Symbolic Model Checker). As an important feature of the proposed method, it does not change the Event-B syntax or semantics. To evaluate this work, as a case study, the Zeroconf protocol will be modeled in the extended UML-B using the Rodin tool, and its Event-B counterpart is converted to a PRISM model. The results of evaluations indicate that this study's additions provide the capability of modeling and verification of probabilistic and stochastic systems.
reference: Vol. 38, 2019, No. 1, pp. 85–114