Evaluating probabilistic models with uncertain model parameters

Probabilistic models are commonly used to evaluate quality attributes, such as reliability, availability, safety and performance of software-intensive systems. The accuracy of the evaluation results depends on a number of system properties which have to be estimated, such as environmental factors or system usage. Researchers have tackled this problem by including uncertainties in the probabilistic models and solving them analytically or with simulations. The input parameters are commonly assumed to be normally distributed. Accordingly, reporting the mean and variances of the resulting attributes is usually considered sufficient. However, many of the uncertain factors do not follow normal distributions, and analytical methods to derive objective uncertainties become impractical with increasing complexity of the probabilistic models. In this work, we introduce a simulation-based approach which uses Discrete Time Markov Chains and probabilistic model checking to accommodate a diverse set of parameter range distributions. The number of simulation runs automatically regulates to the desired significance level and reports the desired percentiles of the values which ultimately characterises a specific quality attribute of the system. We include a case study which illustrates the flexibility of this approach using the evaluation of several probabilistic properties.