This paper proposes a macroscopic model to describe the equilibrium distribution of passenger arrivals for the morning commute problem in a congested urban rail transit system. We use a macroscopic train operation sub-model developed by Seo et al (2017a,b) to express the interaction between the dynamics of passengers and trains in a simplified manner while maintaining their essential physical relations. The equilibrium conditions of the proposed model are derived and a solution method is provided. The characteristics of the equilibrium are then examined through analytical discussion and numerical examples. As an application of the proposed model, we analyze a simple time-dependent timetable optimization problem with equilibrium constraints and reveal that a "capacity increasing paradox" exists such that a higher dispatch frequency can increase the equilibrium cost. Furthermore, insights into the design of the timetable are obtained and the timetable influence on passengers' equilibrium travel costs are evaluated.