Efficient Probabilistic Parameter Synthesis for Adaptive Systems

Probabilistic modelling has proved useful to analyseperformance, reliability and energy usage of distributed ornetworked systems. We consider parametric probabilistic models,in which probabilities are specified as expressions over a setof parameters, rather than concrete values. We address theparameter synthesis problem for parametric Markov decisionprocesses and parametric Markov reward models, which asks fora valuation for the parameters such that the resulting (concrete)probabilistic model satisfies a given property. To solve parametricprobabilistic models for quantitative reachability properties, wepropose efficient, robust methods, either based on sampling, forwhich we provide two algorithms, Markov chain Monte Carloand the cross entropy algorithm, or on swarm intelligence, forwhich we adapt the particle swarm algorithm, a nonlinear opti-misation method from evolutionary computation. We implementthe methods in PRISM and demonstrate the effectiveness of ourapproach on several case studies, including adaptive systems andonline model repair.