Efficient Probabilistic Parameter Synthesis for Adaptive Systems

Probabilistic modelling has proved useful to analyse performance, reliability and energy usage of distributed or networked systems. We consider parametric probabilistic models, in which probabilities are specified as expressions over a set of parameters, rather than concrete values. We address the parameter synthesis problem for parametric Markov decision processes and parametric Markov reward models, which asks for a valuation for the parameters such that the resulting (concrete) probabilistic model satisfies a given property. To solve parametric probabilistic models for quantitative reachability properties, we propose efficient, robust methods, either based on sampling, for which we provide two algorithms, Markov chain Monte Carlo and the cross entropy algorithm, or on swarm intelligence, for which we adapt the particle swarm algorithm, a nonlinear optimisation method from evolutionary computation. We implement the methods in PRISM and demonstrate the effectiveness of our approach on several case studies, including adaptive systems and online model repair.