Robust Model Checking with Imprecise Markov Reward Models

Abstract

Because of the widespread diffusion of computational systems of stochastic nature, in recent years probabilistic model checking has become an important area of research. However, despite its great success, standard probabilistic model checking suffers the limitation of requiring a sharp specification of the probabilities governing the model behaviour. Imprecise probability theory offers a natural approach to overcome such limitation by a sensitivity analysis with respect to the values of these parameters. However, only extensions based on discrete-time imprecise Markov chains have been considered so far for such a robust approach to model checking. Here we present a further extension based on imprecise Markov reward models. In particular, we derive efficient algorithms to compute lower and upper bounds of the expected cumulative reward and probabilistic bounded rewards based on existing results for imprecise Markov chains. These ideas are finally tested on a real case study involving the spenddown costs of geriatric medicine departments.