Capacity utilization affects not only travel times but also delays,
since high capacity utilization increases knock-on delay effects. In
practice,this is partly compensated for by adding buffer times to the
timetable travel times. We have not included delay effects in the
example, but analytically we can interpret the travel times in the
example as if they include buffer times and average delays (valued by
an appropriate multiplier). In the above example we have assumed
capacity constraints, but it is easy to show that the analysis is sensitive
to timetable assumptions also where there are no capacity constraints,
and the investment only reduces travel time. For capacity improvements the analysis is, however, particularly sensitive since the added
capacity can allow for different improvements: travel times, frequencies or reliability.