For scheduled services with relatively high reliability and long headways, most common approach is the “expected delay” approach, where passengers are assumed to value a possible delay proportional to its expected value. Common measures of travellers’ valuations are the “value of [expected] delay time”, or the “reliability multiplier”, i.e. the ratio of the value of delay time to the value of (scheduled) travel time.

Using three different data sets, we investigate whether the expected delay approach holds empirically. In particular, we study how the valuation of apossible delay with probability p and length L depends on p and L.

The main result is that this valuation is not proportional to the expected delay pL, but increases slower than linear in the delay probability. This is particularly pronounced for small risks.

This means that estimated “values of delay time” will depend on the delay risk level p; “delay time values” will be higher the lower the risk level p is. One implication is that estimated values of delay times which does not take the non-linearity in delay risk into account will result in valuations that cannot be transferred between contexts with different delay risks. We also give a theoretical reason why this should be an expected phenomenon, as long asheadways are large.

Regarding the dependence on delay length L, results are ambiguous: in one study, the valuation is linear in delay length L, whereas in another it increases slower than linearly.