Quantifying out-of-station waiting time in oversaturated urban metro systems

Metro systems in megacities such as Beijing, Shenzhen, and Guangzhou are under great passenger demand pressure. During peak hours, it is common to see oversaturated conditions (i.e., passenger demand exceeds network capacity) and a popular control intervention is to restrict the entering rate by setting up out-of-station queueing with crowd control barriers. The out-of-station waiting can make up a substantial proportion of total travel time but is often ignored in the literature. Quantifying out-of-station waiting is important to evaluating the social benefit and cost of metro services; however, out-of-station waiting is difficult to estimate because it leaves no trace in smart card transactions of metros. In this study, we estimate the out-of-station waiting time by leveraging the information from a small group of transfer passengers—those who transfer from nearby bus routes to the metro station. Based on the transfer interval of this small group, we infer the out-of-station waiting time for all passengers by a Gaussian Process regression and then use the estimated out-of-station waiting time to build queueing diagrams. We apply our method to the Tiantongyuan North station of Beijing metro; results show that the maximum out-of-station waiting time can reach 15 ​min, and the maximum queue length can be over 3000 passengers. We find out-of-station waiting can cause significant travel costs and thus should be considered in analyzing transit performance, mode choice, and social benefits. To the best of our knowledge, this paper is the first quantitative study for out-of-station waiting time.