As public transportation faces increasing ridership demand, metrics such as the number of passengers denied boarding become important for measuring the service quality of transit systems. Many studies in the past have used automated fare collection (AFC) (also known as smart card data) and automated vehicle location data to infer the probability distributions for commuters that experience unable-to-board (UTB) events in metro systems, but few have studied UTB events for buses. In this paper, we demonstrate that the probability distribution of UTB commuters inferred from AFC data can be modelled by a truncated binomial distribution under certain assumptions. This model is then validated against synthetic UTB events generated using simulations and against actual UTB events recorded from ground surveys. Finally, we apply our model on real AFC data of commuters in the Singapore bus network to serve as a case study. Our method enables transport planners and operators to identify bus stops and time intervals where overcrowding and UTB events is prevalent, so that appropriate measures can be taken to mitigate such occurrences.

随着公共交通面临日益增长的乘客需求，拒绝登机的乘客数量等指标对于衡量公交系统的服务质量变得很重要。过去的许多研究都使用自动售票机 (AFC)（也称为智能卡数据）和自动车辆位置数据来推断地铁系统中遇到无法登机 (UTB) 事件的通勤者的概率分布，但很少已经研究了公共汽车的 UTB 事件。在本文中，我们证明了从 AFC 数据推断出的 UTB 通勤者的概率分布可以通过某些假设下的截断二项分布来建模。然后针对使用模拟生成的合成 UTB 事件以及根据地面调查记录的实际 UTB 事件验证该模型。最后，我们将我们的模型应用于新加坡公交网络通勤者的真实 AFC 数据，作为案例研究。我们的方法使交通规划者和运营商能够识别过度拥挤和 UTB 事件普遍存在的公交车站和时间间隔，以便采取适当的措施来减少此类事件的发生。