|Title||The two-train separation problem on non-level track|
|Presenter||Amie Albrecht (University of South Australia)|
|Author(s)||Amie Albrecht, Phil Howlett, Peter Pudney, Xuan Vu and Peng Zhou|
|Session||Operations Research and Optimisation|
When two trains travel along the same track in the same direction it is a common safety requirement that they cannot simultaneously occupy the same section of track. In this talk we find necessary conditions on non-level track to minimize the total traction energy required for both trains to complete their respective journeys within the allowed time subject to safe separation constraints in the form of a prescribed set of latest allowed section exit times for the leading train and a corresponding prescribed set of earliest allowed section entry times for the following train. We use classical methods of constrained optimization to show that the optimal driving strategies subject to the sets of prescribed section clearance times are completely defined for the leading train by a non-increasing sequence of optimal section driving speeds and for the following train by a non-decreasing sequence of optimal section driving speeds. We illustrate our results by finding the optimal driving strategies and associated speed profiles for both the leading train and the following train in an elementary but realistic example.
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