Robust Model Checking with Imprecise Markov Reward Models

In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the limitation of requiring a sharp specification of the probabilities governing the model behaviour. The theory of imprecise probabilities 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. 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 tested on a real case study involving the spend-down costs of geriatric medicine departments.

Automated summary

Probabilistic model checking is crucial for computational systems with stochastic nature. Imprecise probabilities and imprecise Markov reward models provide a robust approach to overcome limitations in standard probabilistic model checking by considering uncertainty and sensitivity analysis. Efficient algorithms for computing lower and upper bounds of expected rewards in real-world cases have been developed based on these concepts.