This paper proposes an analytical framework for the scheduling decisions of road travellers that takes into account probability weighting using rank-dependent utility theory. The fundamental difference with the standard scheduling model based on expected utility is that the probabilities of arrivals are treated in a non-linear way. This paper shows how scheduling decisions are affected by the weighted probabilities of the traveller. We derive the costs of non-optimal chosen departure times because of probability weighting and show that if the parameterised probability weighting function is similar to what has been found for gambling, the costs of probability weighting for morning peak car travellers are around 3 per cent. For the full range of parameters tested, we find costs in the range of 0–24 per cent of total travel costs.