The design of modern network-on-chip (NoC) systems faces reliability challenges due to process and environmental variations. Peak power supply noise (PSN) in the power delivery network of a NoC device plays a critical role in determining reliable operations: PSN typically leads to voltage droop, which can cause timing errors in the NoC router pipelines. Existing simulation-based approaches cannot provide rigorous, worst-case reliability guarantees on the probabilistic behaviors of PSN. To address this problem, this paper takes a significant step in formally analyzing PSN in modern NoCs. Specifically, we present a probabilistic model checking approach for the rigorous characterization of PSN for a generic central router of a large mesh-NoC system, under the Round Robin scheduling mechanism with a uniform random network traffic load. Defining features for PSN are extracted at the behavioral level to facilitate property formulation. Several abstract models have been derived for the central router’s concrete model based on the observations of its arbiter’s conflict resolution behavior. Probabilistic modeling and verification are performed using the Modest Toolset. Results show significant scalability of our abstract models, and reveal key PSN characteristics that are indicative of NoC design and optimization.