| Two basic characteristics can be found in a train scheduling (off-line) problem, the huge discrete solving scale, and the periodic cycle implied in the schedule. According to the modeling c of discrete event dynamic systems (DEDS), the running trajectories of trains are divided into discrete events series by railway network units, which is the most fundamental method to research train scheduling problem via discretization of train through a set of critical event. On the other hand, the relevant studies on periodic event scheduling problem (PESP) are important methods to makeup periodic train timetable. Although being different from regular train timetable in the meaning of "periodic", PESP theory provides methodology support for the description of periodic events. A train scheduling problem is regarded as a NP problem in nature, and the analytical form of undetermined solutions becomes rarely found. With the research on ordinal optimization theory of train scheduling and ordinal relation analysis of train overtaking behavior, it is known that the event value is not important sometimes. As the train sequence is given, the solutions can be work out in a fixed polynomial time that are optimal for the train sequence or proved to be unfeasible. As ordinal optimization problem eventually is converted to event time point value model for solution, a reflec-tion is stimulated about the relationship between the train in train diagram and the implied periodic feature, mentioned previously.Based on a combination of DEDS and PESP Train Working Diagram methodolog-ies and ordinal train scheduling theory, Periodic Event System concept is defined and modeling of the relationship between trains is proposed. By these preliminary studies, high-speed railway train scheduling problem is discussed. Briefly, the work and innova-tion are reflected in the following aspects:(1)With the reference of DEDS and PESP train scheduling conception and theore-tical basis, a novel methodology named Periodic Event System (PES) is proposed and defined, which concentrates on the discrete and periodic nature of a train schedule. The PES can be regarded as a finite set of discrete events, occurring constantly along the direction on a periodic ring with a fixed periodic value T. Relative to existing research, PES focuses on the ordinal shaft of the periodic events, especially for the adjoining events. With description mechanism of periodic ring and vectors defined, two analysis equations called periodic events equation and periodic vectors equation are provided as elementary tools, expressing the core feasible rules and constraints. With this under-standing, a PES generic model and a five-stage problem-solving strategy are given.(2) Three-layer railway network is proposed, forming out of macro network, basic network and micro network to accommodate the schedule modeling strategy in different scenarios. Based on PES analysis methodology and the three-layer network structure, a specific train scheduling theory for high-speed railway is presented. The model is stand-ardized and simplified via double spanning transformation with less complexity and more accessible to the solution. A specific generic algorithm is designed to work out the programming. The validity and feasibility are proved by a sample.(3)For the requirement of high-speed railway organization practice and applica-tion, a template scheduling methodology is presented. The template refers to certain features of train trajectories and relation between trains, which are abstracted from operation rules of railway system or human experience. The PES based train scheduling technique is fairly suited for the template generating. With this regard, some common problems are discussed for template schedule methodology, such as rectangle railway construc tion window, arrival or departure tracks occupation and fixed time constraints.(4) Design and develop a PES based high-speed railway train scheduling computer supported system, integrating theory with practice. |
