<p>Performance modelling in service systems benefits significantly from queueing theory, yet the accuracy of results can vary depending on the assumptions underlying each model. This study examines a real-world railway passenger booking system by statistically analyzing inter-arrival and service times of waitlisted passengers. The observed data diverge from the standard Poisson and exponential distributions, leading to the adoption of a general finite-capacity queueing model with arbitrary arrival and service distributions. Queue performance indicators such as expected waiting time and queue length are estimated under this general framework. For comparison, the same parameters are also computed using the classical Markovian multi-server finite-capacity model that assumes exponential behavior. Results reveal substantial differences between the two approaches, particularly in medium- and high-capacity systems, where simplified assumptions lead to notable inaccuracies. This study contributes to the academic literature by empirically validating the performance limits of traditional queueing models under realistic conditions. From a managerial perspective, it provides a more reliable basis for operational decisions involving staffing, scheduling, and system design. On a broader scale, the research holds societal relevance by supporting more efficient and equitable public service delivery in sectors such as transportation through the use of data-driven, empirically justified queueing models.</p> Graphical abstract <p></p>