This study focuses on single variable optimization approaches which determine the holding time of a vehicle when it is ready to depart from a bus stop. Up to now, single variable optimization methods resort to rule-based control logics to equalize the inter-departure headways or adhere to the target headway values. One of them is the two-headway-based control logic which determines the holding time of a bus based on its headway with its preceding and following bus without addressing other implications, such as overcrowding. To rectify this, we introduce a new model for the single variable bus holding problem that considers the passenger demand and vehicle capacity limits. Then, we reformulate this problem to an easier-to-solve program with the use of slack variables and introduce an analytic solution that can determine the holding time of a vehicle at the respective bus stop. Our analytic solution does not add a computational burden to the two-headway-based control logic and can be applied in real time. The operational benefit of our bus holding approach compared to other analytic solutions that do not consider the vehicle capacity is investigated using actual data from bus line 302 in Singapore.

这项研究的重点是单变量优化方法，这些方法确定了车辆准备好离开公交车站时的保持时间。到目前为止，单变量优化方法诉诸于基于规则的控制逻辑，以均衡离港间隔或遵守目标间隔值。其中之一是基于双向的控制逻辑，该逻辑根据总线的前向和后向总线的车距确定总线的保持时间，而无需解决其他问题，例如拥挤。为了解决这个问题，我们针对考虑乘客需求和车辆容量限制的单变量公共汽车持有问题引入了一种新模型。然后，我们使用松弛变量将该问题重新表述为易于解决的程序，并引入了一种解析解决方案，可以确定车辆在各个公交车站的停留时间。我们的解析解决方案不会为基于双向的控制逻辑增加计算负担，并且可以实时应用。与其他不考虑车辆载量的分析解决方案相比，我们的公交拥挤方法的运营优势是使用来自新加坡302号公交线路的实际数据进行调查的。