A parametric model of the train delay distribution to improve planning of heavy haul cycle times

Efficient heavy haul operations require accurate predictions of terminal arrival times and equipment cycle times. Most analytical and parametric approaches for railway capacity evaluation and operations planning focus on predicting average train delay and not the performance of individual trains and their delay distribution. In practice, train delay varies about this average according to some distribution and the cycle-time performance of certain heavy haul trains may be far from average. Using average values of train delay and cycle time during the creation of a heavy haul operations plan may lead to erroneous conclusions that impact the stability of train operations. To address this shortcoming, this research developed a parametric model for predicting the distributions of train delay on single-track mainlines. The new train delay distribution model is based on a set of indices developed to measure both the amount of traffic and the degree of traffic heterogeneity (differences in train speed and priority) present on the route under study. A quantile regression approach was used to build the model since existing statistical distributions could not adequately represent typical train delay distributions within heterogeneous railway traffic. The developed model can be used to assess the impact of changes in traffic mixture (number of high, medium and low priority trains) and train parameters (speed and priority) on the train delay distribution.