The CapTA model is developed to capture the capacity phenomena in passenger traffic assignment to a transit network. These pertain to the interaction of passenger traffic and vehicle traffic: vehicle seat capacity drives the internal comfort, vehicle total capacity determines internal comfort and also platform waiting, passenger flows at vehicle egress and access interplay with dwell time, dwell time drives track occupancy and in turn the period frequency of any service that passes the station along the line of operations, and then service frequency influences service capacity and platform waiting. The RER A - the busiest commuter rail line in Paris- is provided as an application instance to serve as a showcase of the models capabilities and as a means to test its behavior. Some assignment results are showed for the line as a whole, but further analysis is focused on the busier westbound service, where 30 trains/hour can carry around 60,000 passengers/hour. The effect of a greater-than-scheduled dwell time on the service frequency is highlighted for the dense central trunk. The application instance sheds light to the characteristics of the passenger stock waiting and the bottleneck created when demand exceeds available capacity. The westbound trips ending at La Defense business district are used to demonstrate the relative weight of the waiting time and the in-vehicle comfort on the generalized time and the paradox implied. The model is used to give some indications of the expected gains of replacing the actual one-level trainsets with more spacious duplex ones.