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We study the accurate and efficient computation of the expected number oftimes each state is visited in discrete- and continuous-time Markov chains. Toobtain sound accuracy guarantees efficiently, we lift interval iteration andtopological approaches known from the computation of reachability probabilitiesand expected rewards. We further study applications of expected visiting times,including the sound computation of the stationary distribution and expectedrewards conditioned on reaching multiple goal states. The implementation of ourmethods in the probabilistic model checker Storm scales to large systems withmillions of states. Our experiments on the quantitative verification benchmarkset show that the computation of stationary distributions via expected visitingtimes consistently outperforms existing approaches - sometimes by severalorders of magnitude.

Accurately Computing Expected Visiting Times and Stationary Distributions in Markov Chains