Modeling and managing congested transit service with heterogeneous users under monopoly

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 vehicular 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.