Train dwell time models for crowded metro stations using a bivariate distribution function

Train dwell times at high-passenger-volume stations are complex and inconsistent due to variations in passenger behaviour and interactions. While several studies have examined factors affecting dwell time and developed models to predict it, these models often struggle to accurately predict dwell times under high passenger volume conditions. This poses significant challenges to planning effective timetables in crowded environments. Given this variability, using probability-based approaches to predict dwell time delay could provide better planning. Although some studies have identified dwell time probability distribution functions, they generally do not include passenger volume level as a variable, limiting their applicability in high-density stations.

This paper investigates actual operational data to present the limitations of predicting dwell times at high-passenger-volume stations. To address the gap, this paper proposes a bivariate probability function that incorporates passenger volume as a key variable. This gives us a more reliable framework for predicting dwell time delays in crowded environments. The Kolmogorov-Smirnov (K-S) test is used to validate the bivariate dwell time function. This shows the function's capability to predict the probability of achieving target dwell times, which is essential for planning dwell times. Furthermore, this model can be applied alongside delay impact assessments, facilitating a further risk evaluation framework that can be used to make more informed decisions when setting dwell times in timetables.