Modeling Single-Line Train Operations

Scheduling of trains on a single line involves the use of train priorities for the resolution of conflicts. First, a mathematical programming model is described. The model schedules trains over a single line of track when the priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay. This priority is used in a branch-and-bound procedure to allow the determination of optimal solutions quickly. This is demonstrated with the use of an example. Rail operations over a single-line track require the existence of a set of sidings at which trains can cross or overtake each other. Investment decisions on upgrading the numbers and locations of these sidings can have a significant impact on both customer service and rail profitability. Sidings located at insufficient positions may lead to high operating costs and congestion. Second, a model to determine the optimal position of a set of sidings on a single-track rail corridor is described. The sidings are positioned to minimize the total delay and train operating costs of a given cyclic train schedule. The key feature of the model is the allowance of nonconstant train _velocities and nonuniform departure times.