Deadlock analysis, prevention and train optimal travel mechanism in single-track railway system

• We analyze the formation mechanism of train deadlock in the single-track railway corridor.
• The mathematical formulation for the TSCP reflects the variable sensitivity of trains on delay.
• The description of station capacity avoids the discretization of the time horizon.
• A deadlock check procedure is proposed to guarantee occurrence of no deadlock.
• The conflicts–distribution–prediction analyzes the near-optimal travel decisions of trains.

In this paper, train scheduling problem (TSCP) is discussed for the case of single-track railway corridor, in which variable sensitivity on train delay are discussed in detailed for different types of trains. The mathematical model is a complicated nonlinear mixed-integer programming. The object of the model reflects sensitivity of trains with different types or travelling mileages on delay. A heuristic method based on the global conflicts distribution prediction (CDP) is presented. In the CDP, two critical problems restricting the development of simulation method, i.e., train deadlock and near-optimal travel strategy of train, are effectively solved. Numerical experiments show that the CDP can obtain a solution close enough to the optimal solution within a very short computational time. Variable cost weight with trapezoid-shape structure is investigated. Compared with constant weight, the schedule plan has more rational structure when variable cost weight is adopted.