Recently, Harrod has revealed that the occupancy constraints are not sufficient to timetable rail traffic. This insufficiency occurs when opposite movements of trains share the same route. In this paper, we propose a quick algorithm that considers overtaking and opposite train’s movements. This algorithm builds a train timetable from a proposed sequence of trains. It is based on an elementary model of an invariant resource sharing system. The algorithm is proposed in order to extend the genetic algorithm that calculates the sequence of trains for maximizing the frequency of passenger’s train.

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