In urban mass transit, station platforms constitute waiting area for incoming users users willing to board service vehicles. In the transit bottleneck model of Leurent et al. (2014, 2015), the passenger stocks and average wait times according to station of destination are obtained as the solution of a fixed point problem (FPP) with respect to passenger stocks: multiple service routes are allowed, each of which with residual in-vehicle capacity that can be or not saturated by the flow of users incoming at the station of interest. The paper provides a full sensitivity analysis of all model outcomes to all model inputs, namely entry flows according to destination stations, residual in-vehicle capacities and route frequencies. The method consists in partial differentiation by formal calculus, since the FPP amounts to an implicit function that is differentiable almost everywhere. As instance of application, the case of a busy commuter rail line in Paris is studied, with emphasis on the marginal congestion costs of incoming as well as on-board users onto the users waiting for boarding.