Analysing Train Delay Impacts on Subway Stations via a Three-stage Approach: An Empirical Study on Shanghai Metro

Abstract Delays can adversely affect passengers, operational efficiency, and punctuality, necessitating effective methods to identify and analyse stations vulnerable to such delays. This study proposes a three-stage analytical framework. In the first stage, the 3σ rule is utilized to define normal passenger volume ranges and establish a specific time window, focusing on periods significantly affected by delays. Next, a multivariate time series clustering method is proposed to identify stations with stable demand and high volume, considering passenger volume differences both among and within stations. In the final stage, the effects of delays on these key stations are assessed by examining duration, starting, and ending times, and passenger volume variation, providing a comprehensive analysis of delay impact. The proposed method is validated on a real-world case: the 2021 delay incident at Shanghai Metro's Longyang Road Station. Our case study revealed that stations significantly impacted by delays are not limited to the specific line or direction of the delay, but also include opposite direction and network transfer stations. The starting time of effects at stations occurs in three stages—prior to, during, and after the delay—with full recovery at most key stations not occurring until the third time window. Additionally, both increases and decreases in passenger volumes due to the delay present considerable implications. Our results aid transit managers in better managing delays, thereby improving passenger satisfaction and operational efficiency. This paper also offers a comprehensive framework and an empirical study, providing valuable guidance for future research in this area.