Verifying that a stochastic system is in a certain state when it has reached equilibrium has important applications. For instance, the probabilistic verification of the long-run behavior of a safety-critical system enables assessors to check whether it accepts a human abort-command at any time with a probability that is sufficiently high. The stochastic system is represented as probabilistic model, a long-run property is asserted and a probabilistic verifier checks the model against the property.

Probabilistic model checking is a formal verification technique that has been applied successfully in a variety of domains, providing identification of system errors through quantitative verification of stochastic system models. One domain that can benefit from probabilistic model checking is cloud computing, which must provide highly reliable and secure computational and storage services to large numbers of mission-critical software systems.

Uncertainty complicates the formal verification of nondeterministic systems. Unpredictable changes and alterations in their environments can lead an invalid verification results and the decrease of confidence degree of these systems. However, current literature provides little account of addressing the uncertainty in formal verification. To address this problem, the goal of this research is to provide a method based on perturbation analysis for probabilistic model checking of nondeterministic systems which are modelled as Markov Decision Processes. And to apply our expected contributions to ubiquitous systems due to inherent presence of environment uncertainty and their resource limitations.