Modelling and Forecasting Passenger Rail Demand in Slovakia Under Crisis Conditions with NARX Neural Networks

Transportation systems are particularly vulnerable to disruptions such as pandemics, which create significant challenges for maintaining efficiency, safety, and service quality. This study focuses on rail passenger transport in the Slovak Republic and develops a simulation framework to evaluate system performance under crisis conditions. Weekly data from the national rail operator for the period 2019–2021 were combined with information on governmental restrictions, standardized into a five-level framework. A nonlinear autoregressive model with exogenous inputs (NARX), implemented and validated in MATLAB R2021b (MathWorks, Natick, MA, USA), was applied to simulate the impact of restrictive measures on passenger demand. The results revealed a strong relationship between the severity of measures and ridership levels, with the most significant effects observed in education, workplace access, movement limitations, and retail. For instance, during complete school closures, passenger volumes declined by up to 75% relative to the pre-pandemic baseline. Based on the simulation outcomes, recommendations were formulated for adapting railway operations, including dynamic adjustments of transport capacity (10–40%) according to restriction levels. The proposed modelling and simulation approach offers transport authorities a cost-effective tool for scenario testing, disruption management, and the design of resilient passenger rail systems capable of adapting to crises and uncertainties.