# Optimizing the train timetable in a high-speed rail corridor: The implications on departure time, fare cost and seat preference of passengers

## TL;DR

This paper introduces a new method for optimizing high-speed rail timetables by considering passenger preferences for departure times, fares, and seat classes.

## Contribution

A novel three-dimensional network model and bi-level programming approach are proposed to balance operator and passenger needs in train scheduling.

## Key findings

- A time-space-state network (TSSN) effectively integrates passenger preferences into train scheduling.
- A bi-level model with user equilibrium theory improves the distribution of passenger demand across trains.
- The proposed method enhances timetable efficiency and passenger satisfaction in the Lanzhou-Xi’an corridor case study.

## Abstract

High-speed railway timetables are typically based on origin-destination (OD) passenger demand, establishing departure times and intervals for trains. Utilizing this data, operators systematically develop daily train timetables that are consistent across a defined operational cycle. However, this approach often overlooks individual passenger preferences for departure times, fares, and seat classes, leading to low occupancy rates for some trains while others remain difficult to book. In this article, with the number of trains predetermined and considering the diverse demands of passengers, we addresses these challenges by analyzing passenger preferences and optimizing train stopping patterns and adjacent train departure intervals. We propose a time-space-state three-dimensional network (TSSN) that integrates preferences for travel time, fares, and seat classes. Impedance functions for various network arcs are developed, incorporating these three key attributes of travel demand and transforming the passenger travel choice issue into a path selection problem within the TSSN. A bi-level programming model is formulated: the upper level optimizes train operations and fare structures, while the lower level employs user equilibrium (UE) theory to distribute OD passenger demands across trains. Using the Lanzhou-Xi’an high-speed railway corridor as a case study, we apply a genetic algorithm combined with a nested Frank-Wolfe method to solve the model. The resulting timetable balances the interests of high-speed rail operators and passengers, incorporating non-uniform departure intervals to better meet diverse travel needs. Ultimately, this approach enhances the scientific rigor and practicality of high-speed railway scheduling while accommodating passenger preferences effectively.