Accurately Computing Expected Visiting Times and Stationary Distributions in Markov Chains

TL;DR

This paper presents a new method for accurately and efficiently computing expected visiting times and stationary distributions in large Markov chains, improving scalability and performance over existing techniques.

Contribution

It introduces an approach combining interval iteration and topological methods for precise computation, applicable to large-scale probabilistic models.

Findings

Outperforms existing methods in computing stationary distributions.

Scales efficiently to systems with millions of states.

Achieves significant speedups, sometimes by orders of magnitude.

Abstract

We study the accurate and efficient computation of the expected number of times each state is visited in discrete- and continuous-time Markov chains. To obtain sound accuracy guarantees efficiently, we lift interval iteration and topological approaches known from the computation of reachability probabilities and expected rewards. We further study applications of expected visiting times, including the sound computation of the stationary distribution and expected rewards conditioned on reaching multiple goal states. The implementation of our methods in the probabilistic model checker Storm scales to large systems with millions of states. Our experiments on the quantitative verification benchmark set show that the computation of stationary distributions via expected visiting times consistently outperforms existing approaches - sometimes by several orders of magnitude.