  An important aspect of the quality of a public transport service is its
reliability, which is defined as the invariability of the service attributes.
Preventive measures taken during planning can reduce risks of unreliability
throughout operations. In order to tackle reliability during the service
planning phase, a key piece of information is the long-term prediction of the
density of the travel time, which conveys the uncertainty of travel times. We
introduce a reliable approach to one of the problems of service planning in
public transport, namely the Multiple Depot Vehicle Scheduling Problem (MDVSP),
which takes as input a set of trips and the probability density function
(p.d.f.) of the travel time of each trip in order to output delay-tolerant
vehicle schedules. This work empirically compares probabilistic models for the
prediction of the conditional p.d.f. of the travel time, as a first step
towards reliable MDVSP solutions. Two types of probabilistic models, namely
similarity-based density estimation models and a smoothed Logistic Regression
for probabilistic classification model, are compared on a dataset of more than
41,000 trips and 50 bus routes of the city of Montr\'eal. The result of a vast
majority of probabilistic models outperforms that of a Random Forests model,
which is not inherently probabilistic, thus highlighting the added value of
modeling the conditional p.d.f. of the travel time with probabilistic models. A
similarity-based density estimation model using a $k$ Nearest Neighbors method
and a Kernel Density Estimation predicted the best estimate of the true
conditional p.d.f. on this dataset.
