Estimating the robustness of train plans for single-line corridors with crossing loops

Abstract

The movement of trains is often planned in advance to determine where and when trains will cross each other, and to determine arrival times for trains at their final destinations. However, random variations to departure times and travel times mean that crosses do not always occur at the planned locations and times, and excessive delays lead to trains arriving late at their destinations. We define the robustness of a train plan to be the expected reliability of that plan when the trains are subjected to typical departure variations and variations in travel speeds, and when standard procedures are used to recover from these delays. Robustness can be estimated by simulating the operation of the network for many different delays, but can we do a more direct calculation? We calculate the distribution of arrival times for a train with random departure and travel times that might be delayed by a second train. References

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