Cities depend on public transit systems. However, the complexity and numerous uncertainties faced by these systems can make it seemingly intractable to cope with unforeseen disruptions. This work presents the analysis of the inherent variability and prediction uncertainty of passenger in- and outflows at stations in an urban rail system. We study data gathered from New York City’s subway system over seven years and develop probabilistic models of the expected passenger flows. We determine the operating envelope over the course of a week, find critical flow levels during specific times of day, and establish fragility curves of the system using a Bayesian approach to estimate the probability of exceeding a critical flow level over the duration of a disruption. In addition, we present a prediction model based on Gaussian Process regression to determine future expected counts of passengers. This approach can be useful for planners and operators in improving the system based on expected platform capacities, assessing the risks associated with everyday operations, reliably forecasting whether the station in- and outflows are expected to remain within the operating envelope, and guiding the deployment of mitigation measures.