## 1 Introduction  
The relatively reliable schedule adherence of railway systems is one of the most attractive merits of the mode for the railway passengers [1]. However, it is still a challenge to operate on railways with perceived reliability. Railway schedules are constructed based on passenger demand, although the arrival patterns of passengers at stations are not uniform or deterministic in real-life. If a particular train's arrival at a station is delayed, an additional accumulation of arriving passengers in the meantime will result in extended boarding and alighting times when the train dwells at the station, and this event will further propagate delays with respect to subsequent trains upstream. Railway operators and authorities have considered different strategies when determining train schedules with respect to stations with expected passenger demands. They employ a \"running time supplement\" [2, 3], a buffering time that can help to recover from delays if they occur. To minimize the delay, larger railway operators often control the passenger demand with a more direct approach of employing dedicated personnel on the platforms at stations, who can restrict passengers from boarding trains when they are delayed. There have been various studies in predicting delays and analyzingtheir intrinsic nature [2; 3], timetable optimization [4; 5; 6; 7], developing appropriate performance indices, and utilizing them for timetable construction [8]. For railway-related research, it is essential to have access to real-life data, including the operation of trains and passenger flows, while a larger amount of data will further benefit the reliability of the analysis. Automatic passenger counters (APCs) and smart card-based fare payment systems have been utilized for such purposes. [PERSON] et al. [9] utilized big data based on the smart card system in Seoul, South Korea for assessing performance measures of the public transit services including schedule adherence and crowdedness of passengers. Using smart card-based passenger fare and rail operation data, [PERSON] et al. [10] developed models for predicting actually taken passenger-routes, the number of boarding and alighting passengers at stations, and the number of passengers on board between stations. [PERSON] et al. [11] used data from Line 1 of the Panama Metro and passengers' preferences of train ticket classes in order to estimate dwell times at each station. [PERSON] et al. [12] developed a regression model to investigate the relationship between dwell time and the number of boarding and alighting passengers, and tested it using Monte-Carlo simulations. [PERSON] et al. [13] developed a timetable adjustment model for the Hong Kong metro, MTR, by analyzing the departure and arrival information of trains, boarding and alighting passenger counts at stations, and historical data of past causes of delays. [PERSON] et al. [14] developed a machine learning model based on a support vector regression method for predicting delays at railway stations operated with different classes of trains. [PERSON] and [PERSON] [15] proposed a regression-based estimation model for future train delays using only the operation records of trains. Despite numerous efforts in research works regarding train delays, there have not been any significant research works for modeling dwell/delay time of trains utilizing boarding and alighting passenger counts, or onboard crowdedness (load factor), for all trains at all train stations of a metro line. [PERSON] et al. [16] conducted a similar line of research for Line 8 of the Shanghai Metro in China, yet with limited data and simulated values for load factor, boarding, and alighting passenger counts. [PERSON] et al. [17] adopted a Gompertz curve to overcome a limited data set of boarding and alighting passenger counts collected at 30-min intervals.