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This paper proposes a macroscopic model to describe the equilibriumdistribution of passenger arrivals for the morning commute problem in acongested urban rail transit system. We use a macroscopic train operationsub-model developed by Seo et al (2017a,b) to express the interaction betweenthe dynamics of passengers and trains in a simplified manner while maintainingtheir essential physical relations. The equilibrium conditions of the proposedmodel are derived and a solution method is provided. The characteristics of theequilibrium are then examined through analytical discussion and numericalexamples. As an application of the proposed model, we analyze a simpletime-dependent timetable optimization problem with equilibrium constraints andreveal that a "capacity increasing paradox" exists such that a higher dispatchfrequency can increase the equilibrium cost. Furthermore, insights into thedesign of the timetable are obtained and the timetable influence on passengers'equilibrium travel costs are evaluated.

Morning commute in congested urban rail transit system: A macroscopic model for equilibrium distribution of passenger arrivals