We analyse congestion pricing in a road and rail network with heterogeneous users. On the road there is bottleneck congestion. In the train there is crowding congestion. We separately analyse "proportional heterogeneity" that varies the values of time and schedule delay scalarly in fixed...

In most dynamic traffic congestion models, congestion tolls must vary continuously over time to achieve the full optimum. This is also the case in Vickrey's (1969) 'bottleneck model'. To date, the closest approximations of this ideal in practice have so-called 'step tolls,' in which the toll...