This paper deals with the scheduling of trains so as to minimize train
trip times while maximizing reliability of arrival times. The amount
of risk of delay (RD) associated with a schedule is used as the reliab
ility component of a constrained schedule optimization model. The pape
r outlines the model developed to quantify the risk of delays to indiv
idual trains, as well as to specific track segments and to the schedul
e as a whole. The risk model, which deals with single track operations
, can be used to estimate the likely impact on reliability of arrival
times, changes in train frequencies, and operating practices; track an
d station infrastructure investment strategies; and train technology u
pgrading. An application of the model to the optimization of schedules
on a track corridor is described. The results obtained using the mode
l are compared with the schedules used by train operations planning st
aff, in terms of overall delay and timetable reliability. The results
highlight the significance of including a measure of timetable reliabi
lity, such as risk of delays, in the objective function for scheduling
optimization.