Wenbo Fan

Timetables are crucial for the efficient operation of public transportation. This paper tackles the timetabling problem of a regular bus line facing oversaturation due to stochastic fluctuation in demand and a lack of fleet, making it more complex than traditional undersaturated scenarios. By oversaturation, we mean some passengers may not board the first‐arrival bus and must wait for subsequent ones. We propose a reinforcement learning (RL) model based on the Markov decision process (MDP) to optimize the timetable. The objective is to minimize the expected total system costs, involving the costs of passengers and the operator. Constraints concerning vehicle capacity and fleet size are respected. The dynamics of passengers are captured in the state transition process. The proposed model is applied to the No. 8 bus route in Sanya, China. Specifically, the proximal policy optimization (PPO) algorithm is employed. Under deterministic demand, we compare the optimized timetables against the results obtained by classic models. The results show that the proposed model outperforms classical models in terms of both solution quality and computational efficiency. Under stochastic demand, as variance in demand increases, the benefit of the proposed model in the system cost and passenger waiting time becomes more significant. In addition, we optimize the fleet size, accounting for the acquisition cost of vehicles.

Modeling passenger route choices is crucial for analyzing and predicting public transportation demand. One of the most popular methods is to use probabilistic route choice (PRC) models (also known as discrete choice models in general), which have broad applications in transportation, economics, politics, and other fields. However, its performance varies depending on the characteristics of the origin–destination (OD) trip data and should be examined carefully. This paper proposes a framework for validating the PRC model on its application to urban rail transit (URT) networks containing small‐scale OD trip data. The concept of small‐scale data is defined at first for each OD pair considering the desired confidence level and the variance of route choices. Then, a travel time range (TTR)‐based method is put forward to deduce passengers’ actual route choices as a benchmark for verifying PRC models. The difference and regularity analysis between the actual route choices and the model predictions are also performed with a twofold comparison. A case study on the Nanchang metro in China shows that the actual daily passenger volumes on routes of small‐scale OD pairs diverge remarkably from the estimations of the PRC model. The PRC model’s performance is further discussed when the small‐scale OD trip data accumulate to a larger scale over multiple days (e.g., several months). This study reveals the inherent limitation of PRC models in estimating the travel behaviors of passengers in a small‐scale population. Several practical implications are discussed to improve the route choice model and passenger flow analysis.