Scheduling Trains on Parallel Lines with Crossover Points

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In this article a sequencing approach is proposed for train scheduling on parallel lines separated by crossover points. The primary feature that is introduced is a modeling device called a compound buffer that is very powerful, particularly because it has widespread applicability. It may be used to maintain the correct occupancy levels of lines while allowing trains to pass through the crossover points without additional routing decisions. The compound buffer is a collection of machines that collectively acts as a traditional capacitated buffer. The machines that are part of the compound buffer, however, maintain their independence and are not treated differently in the scheduling process. To demonstrate the validity and effectiveness of this new approach, a variety of typical railway infrastructure were considered. Extensive numerical investigations show that the approach successfully and consistently creates train schedules of high quality. It also shows that compound buffers accurately portray the technical constraints of the real system.