Asymptotic Bounds for Quantitative Verification of Perturbed Probabilistic Systems
This work addresses the challenge of robust verification for real-life probabilistic systems where parameters are subject to measurement errors, offering incremental improvements in sensitivity analysis for domain-specific applications.
The paper tackles the problem of verifying reachability probabilities in probabilistic systems with uncertain distribution parameters, providing a method to compute asymptotic bounds (condition numbers) for these probabilities under small perturbations, demonstrated through experiments on the Zeroconf protocol and hopping frog problem.
The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained by empirical measurements and thus are subject to small perturbations. In this paper, we consider perturbation analysis of reachability in the parametric models of these systems (i.e., parametric Markov chains) equipped with the norm of absolute distance. Our main contribution is a method to compute the asymptotic bounds in the form of condition numbers for constrained reachability probabilities against perturbations of the distribution parameters of the system. The adequacy of the method is demonstrated through experiments with the Zeroconf protocol and the hopping frog problem.