In this paper, we propose a method for estimating the timings at which trains arrive and depart from stations using passenger farecard data and knowledge of the network topology. The problem we consider is essential for understanding commuter movement patterns across metro systems at high granular detail in settings where one does not have access to train logs (comprising records of train arrival and departure timings) or when these records are unreliable. Our technique requires as input the timings at which passengers arrive and depart from station—these are easily retrievable from farecard data—and provide as output an estimate of the number of trains running as well as the timings at which each train arrives and departs at each station. Our method relies on two key observations: (1) passengers tend to exit metro stations as soon as they alight and (2) we can reliably conclude that groups of passengers who board at the same stop but alight at different stops were on the same train if their boarding timings have similar distributions. In contrast with prior works, our methodology is stand-alone in that it does not rely on external sources of information such as train schedules and it requires minimal parameter tuning. In addition, because a by-product of our method is that we infer the trains for which passengers board, our techniques can be employed as a pre-processing step for downstream tasks such as inferring passenger route choices. We apply our method to recover train logs using synthetically generated data as well as actual ticketing data of passengers in the Singapore metro network. Experiments on synthetic data show that our method reliably recovers train logs even with moderate levels of overcrowding on train platforms.

在本文中，我们提出了一种使用旅客票价卡数据和网络拓扑知识来估算列车到达和离开车站的时刻的方法。我们所考虑的问题对于在无法访问火车日志（包含火车到达和离开时间的记录）或这些记录不可靠的环境中，以高精细度的细节了解地铁系统中通勤者的交通方式至关重要。我们的技术需要输入乘客到达和离开车站的时间（可以很容易地从车票卡数据中获取）作为输入，并提供输出信息，以估算运行的火车数量以及每列火车到达和离开的时间站。我们的方法依赖于两个关键的观察：（1）乘客往往在下车后便离开地铁站；（2）我们可以可靠地得出结论，如果他们的上车时刻具有相似的分布，那么在同一站点上车但在不同站点下车的乘客群在同一列火车上。与以前的工作相比，我们的方法是独立的，因为它不依赖外部信息源（例如火车时刻表），并且需要的参数调整最少。另外，由于我们方法的副产品是我们推断出乘客登上的火车，因此我们的技术可以用作诸如推断乘客路线选择之类的下游任务的预处理步骤。我们使用我们的方法使用综合生成的数据以及新加坡地铁网络中乘客的实际票务数据来恢复火车日志。