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本文从系统论的角度,提出了一种大型铁路网络中列车运行限制状态的空间模型。本文的创新性是将网络有向图变换或者简化为并行列表,这就避免了将这一复杂问题的数学处理。这个模型考虑了真实网络(例如德国铁路)中的各个方面。系统的操作引入了自由度和鲁棒性,这样,大型网络中列车运行时间最优问题可以用极大值原理来定义和解决。通过把时间最优准则引起的边值问题简化为常微分方程的初值,从而可以得到问题的解答。本文对控制过程中所有可能的转换点进行了分类。预计本文提出的方法可以实现大型网络中铁路时间最优的超实时仿真并简化网络调度员的实时控制,通过对德国铁路局部网络仿真结果的分析,可以量化地证明预期结果。铁路行业从业者应注意,在许多国家,铁路网络是公共交通系统的核心。为了保证网络运行安全,必须避免交汇或追踪运行列车的相互碰撞,如果仅有一个明确定义的时刻表可能无法解决这个问题,这是因为很多原因会造成无法遵循计划。同样地,一些控制是强制性的,这就要求对现存网络寻求建立一个合适的模型。事实上,本文提出的模型的创新性是将铁路网络的有向图进行变换或者简化,即把有向图简化为与列车数量相同的并行列表,每列列车的列表包括物理参数、路径、时刻表规格说明以及与其他列车相互作用的信息。为了实现网络的在线仿真,所有相互作用的列车的列表均通过轮叫调度的方式并行工作,并且通过解析列车间的相互作用找到它们位置、速度与时间的对应关系。该网络的其余部分的仿真,例如无交互的列车,在离线的情况下可用同样的方式完成。德国铁路局部网络的示例和仿真结果不仅验证了大型网络中时间最优列车运行的建模、分析、综合及仿真中提出的方法的实用性,还验证了模型的以下显著优点:(1)避免或降低了问题的数学复杂性;(2)能满足所有网络的特殊性要求;(3)通用性,也就是说,可以用于新网络建立操作系统;(4)系统操作中引入自由度和鲁棒性;(5)在线仿真能力;(6)定量分析和仿真时间估计;前面的两个特点保证调度员有时间仔细考虑当前状况,以便于采取正确的操作步骤。因此,它也有助于调度员对网络的实时控制。
In this paper, from a system theory point of view, this paper proposes a space model for the limitation of train operation in large railway networks. The innovation of this paper is to transform or simplify the network directed graph into a parallel list, which avoids the mathematical treatment of this complicated problem. This model takes into account all aspects of a real network, such as the Deutsche Bahn. The operation of the system introduces the degree of freedom and robustness. In this way, the optimal train running time in large networks can be defined and solved by the principle of maximum value. By solving the boundary value problem caused by the optimal time criterion to the initial value of the ordinary differential equation, the solution to the problem can be obtained. This article classifies all possible transition points in the control process. It is expected that the proposed method can realize the ultra-real-time simulation of railway time in large-scale networks and simplify the real-time control of network dispatchers. The analysis of the results of local network simulation in German railways can quantitatively prove the expected results. Railway industry practitioners should note that in many countries, the railway network is at the heart of the public transport system. In order to ensure the safe operation of the network, it is necessary to avoid the intersection or tracing of collisions between running trains. If there is only a well-defined schedule, this problem may not be solved. This is because for many reasons, the plan can not be followed. Similarly, some controls are mandatory, which requires seeking to establish an appropriate model of the existing network. In fact, the model proposed in this paper is innovative in that the directed graph of the railway network is transformed or simplified, that is, the directed graph is reduced to a parallel list with the same number of trains. The list of each train includes physical parameters, paths, moments Table specifications and information on interactions with other trains. In order to realize online simulation of the network, the list of all interacting trains work in parallel by way of wheel scheduling, and find the correspondence between their positions, speeds and time by analyzing the interaction among trains. The simulation of the rest of the network, for example without interactive trains, can be done in the same way when offline. The examples and simulation results of the local railway network in Germany not only verify the practicability of the proposed method in modeling, analyzing, synthesizing and simulating the optimal train operation in large networks, but also verify the following significant advantages of the model: (1) avoid Or reduce the mathematical complexity of the problem; (2) can meet the special requirements of all networks; (3) universal, that is to say, can be used to build an operating system in a new network; (4) Robustness; (5) online simulation capabilities; (6) quantitative analysis and simulation time estimation; the first two features ensure dispatchers have time to carefully consider the current situation in order to take the correct steps. Therefore, it also helps dispatchers control the network in real time.