We develop and study a model of congested transit service under monopoly when potential users differ in their characteristics. Given travel time delays and crowding externalities, general user heterogeneity is characterized in a three-dimensional space of value of time, value of crowding, and willingness to pay. A unique user demand equilibrium is shown to exist. The operator chooses the fare and service frequency to maximize a weighted sum of profit and consumers’ surplus. The socially optimal fare consists of marginal operating cost, external user congestion cost, and a nonnegative shadow price on the vehicle capacity constraint which may or may not bind. A cost-recovery formula is also derived. Two methods for optimal design capacity are proposed that differ as to whether fare and frequency are exogenous or set conditional on capacity choice. Two numerical examples, one without and one with crowding, are presented to illustrate the theoretical results.

当潜在用户的特征不同时，我们将研究和研究一种垄断下的拥堵公交服务模型。考虑到旅行时间的延迟和拥挤的外部性，一般用户异质性的特征在于时间价值，拥挤价值和支付意愿的三维空间。显示存在唯一的用户需求平衡。运营商选择票价和服务频率，以使利润和消费者剩余的加权总和最大化。社会最优票价包括边际运营成本，外部用户拥塞成本以及对车辆容量约束的非负影价格，该价格可能会约束也可能不会约束。还推导了成本回收公式。提出了两种优化设计容量的方法，它们关于票价和频率是外生的还是以容量选择为条件而有所不同。