Computing cumulative rewards using fast adaptive uniformisation

The computation of transient probabilities for continuoustime Markov chains often employs uniformisation, also known as the Jensen's method. The fast adaptive uniformisation method introduced by Mateescu approximates the probability by neglecting insignificant states, and has proven to be effective for quantitative analysis of stochastic models arising in chemical and biological applications. However, this method has only been formulated for the analysis of properties at a given point of time t. In this paper, we extend fast adaptive uniformisation to handle expected reward properties which reason about the model behaviour until time t, for example, the expected number of chemical reactions that have occurred until t. To show the feasibility of the approach, we integrate the method into the probabilistic model checker PRISM and apply it to a range of biological models, demonstrating superior performance compared to existing techniques.