Abstract
A substantial literature exists on the estimation of the delay function for a single-track railroad with the assumption that the trains are uniformly distributed over time. In order to make the estimation more accurate and realistic, this paper provides the definition of delay functions for a scheduled railroad in which each train has a scheduled departure and arrival time. The key feature of this paper is that the uncertainty in the actual train departure time is explicitly taken into consideration. Since the variance of delay is important in the measurement of the reliability of a given set of schedules, both the mean and the variance of delay are estimated by solving a system of nonlinear equations.
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