An innovative model for capturing seasonal patterns of train passenger movement using exogenous variables and fuzzy time series hybridization

Train is a popular mode of ground transportation due to the ability to accommodate a large number of passenger, save time, avoid traffic congestion, offer cost-effective fares, and provide a relatively high level of safety. These benefits contribute to an annual increase in passenger numbers, particularly during holidays and the year-end period. Consequently, it is essential for management to anticipate potential capacity constraints faced by train operators. Detecting this challenge encompasses observing train passenger count trends at the end of each year, which can be effectively analyzed using Seasonal Autoregressive Integrated Moving Average (SARIMA) model to account for seasonal effects. Train passenger surges also align with the Eid Al-Fitr holiday in Indonesia, an event that varies annually according to the Hijri calendar. To address this issue, SARIMA was adapted to include exogenous effects in the form of calendar variations, producing Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX). Furthermore, a novel numerical model was proposed using Fuzzy Time Series Markov Chain (FTSMC). Consequently, it is vital for management to anticipate potential capacity constraints that train operators might face. This innovation was introduced through hybrid SARIMA-FTSMC and hybrid SARIMAX-FTSMC. The results showed that hybrid SARIMA-FTSMC delivered the highest accuracy level with the smallest error value, providing more precise insights into train passenger movement patterns. These modeling results also offered valuable recommendations for risk management to address capacity limitations during the Eid Al-Fitr holiday and the year-end period, enabling train operators to optimize the services effectively.