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.