Robust Model Checking with Imprecise Markov Reward Models

TL;DR

This paper extends probabilistic model checking to imprecise Markov reward models, enabling robust analysis of stochastic systems with uncertain probabilities through efficient algorithms and a real-world case study.

Contribution

It introduces a novel extension of model checking using imprecise Markov reward models and develops algorithms for computing bounds on expected rewards.

Findings

Algorithms efficiently compute bounds on rewards.

Application to real-world healthcare case study.

Demonstrates robustness against probability imprecision.

Abstract

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.