Simulation for influence of train failure on railway traffic flow and research on train operation adjusting strategies using cellular automata

Many complex train operation plans are being implemented in practice because more and more railway transit networks have been constructed and put into use, and thus a certain train’s failure will cause more harmful influence on the efficiency and safety of the overall railway transit system. In this paper, a new cellular automaton model is proposed. In this model, two control schemes are introduced to simulate the characteristic behaviors of railway traffic flow when a train breaks down for traction failure, stops, and later be rescued by its first following train. The simulation results prove that the proposed model is able to simulate the occurrence of train failure and reproduce the complex behaviors of train movement in railway transit system. Two train operation adjusting strategies are proposed and tested later with this model. Simulation results show that increments in train operation interval after the train failure bring more benefits than decrements in maximum velocity and that with proper parameters both strategies can serve to reduce the severity of delay and go-and-stop waves to a lower level.     

Properties of train traffic flow in moving block system

The development direction of railway is to improve the capacity and the service quality, where the service quality includes safety, schedule, high speed, and comfort. In light of the existing cellular automaton models, in this paper, we develop a model to analyze the mixed running processes of trains with maximal speeds of 500 km/h and 350 km/h respectively in the moving block system. In the proposed model, we establish some sound rules to control the running process of train, where the rules include the departure rules in the intermediate stations, the overtaking rules, and the conditions of speed limitation for train stopping at a station or passing through a station. With the consideration of the mixed ratio and the distance between two adjacent stations, the properties of the train traffic flow (including capacity and average speed) are simulated. The numerical results show that the interactions among different trains will affect the capacity, and a proper increasing of the spatial distance between two adjacent stations can enhance the capacity and the average speed under the moving block.     

Traffic Modelling for Moving-Block Train Control System

This paper presents a new cellular automaton （CA） model for train control system simulation. In the proposed CA model, the driver reactions to train movements are captured by some updated rules. The space-time diagram of traffic flow and the trajectory of train movement is used to obtain insight into the characteristic behavior of railway traffic flow. A number of simulation results demonstrate that the proposed CA model can be successfully used for the simulations of railway traffic. Not only the characteristic behavior of railway traffic flow can be reproduced, but also the simulation values of the minimum time headway are close to the theoretical values.     

Modeling and Simulation for Urban Rail Traffic Problem Based on Cellular Automata

Based on the Nagel-Schreckenberg model, we propose a new cellular automata model to simulate the urban rail traffic flow under moving block system and present a new minimum instantaneous distance formula under pure moving block. We also analyze the characteristics of the urban rail traffic flow under the influence of train density, station dwell times, the length of train, and the train velocity. Train delays can be decreased effectively through flexible departure intervals according to the preceding train type before its departure. The results demonstrate that a suitable adjustment of the current train velocity based on the following train velocity can greatly shorten the minimum departure intervals and then increase the capacity of rail transit.     

准移动闭塞系统的元胞自动机模型及列车延迟传播规律的研究

在NaSch模型的基础上，针对铁路交通的特点提出一种用于模拟准移动闭塞系统的元胞自动机模型.应用该模型模拟了准移动闭塞系统列车延迟传播的交通现象，分析了准移动闭塞系统中的轨道定位单元长度、发车时间间隔、初始延迟时间等因素对列车延迟传播的影响. 关键词： 元胞自动机 交通流 准移动闭塞     

Modeling and Simulation for Urban Rail Traffic Problem Based on Cellular Automata

Based on the Nagel-Schreckenberg model, we propose a new cellular automata model to simulate the urban rail traffic flow under moving block system and present a new minimum instantaneous distance formula under pure moving block. We also analyze the characteristics of the urban rail traffic flow under the influence of train density, station dwell times, the length of train, and the train velocity. Train delays can be decreased effectively through flexible departure intervals according to the preceding train type before its departure. The results demonstrate that a suitable adjustment of the current train velocity based on the following train velocity can greatly shorten the minimum departure intervals and then increase the capacity of rail transit.     

固定闭塞系统中列车流的特性分析

在NS模型的基础上，针对轨道交通的特点，本文提出一种用于模拟四显示固定闭塞系统的元胞自动机模型.应用该模型模拟四显示固定闭塞系统中的列车延迟的交通现象，分析了四显示固定闭塞系统中的发车时间间隔、客货车比例、车站停靠时间、停靠站台数量等因素对列车平均延迟时间的影响.结果表明：客、货车混行时，货车对后行客车的运行会产生抑制作用，调整客、货车在车站的停靠时间可有效缓解这种抑制作用，减少客车的延迟时间；增加停靠站台的数量可提高线路上的车流密度，缓解车流延误，但在较大的发车时间间隔时，站台的利用率会降低. 关键词： 元胞自动机 固定自动闭塞系统 列车延迟     

Urban rail departure capacity analysis based on a cellular automaton model

As an important traffic mode, urban rail transit is constantly developing toward improvement in service capacity and quality. When an urban rail transit system is evaluated in terms of its service capacity, the train departure capacity is an important index that can objectively reflect the service level of an urban rail transit facility. In light of the existing cellular automaton models, this paper proposes a suitable cellular automaton model to analyze the train departure capacity of urban rail transit under different variable factors and conditions. The established model can demonstrate the train operating processes by implementing the proposed sound rules, including the rules of train departure at the origin and intermediate stations, and the velocity and position updating rules. The properties of train traffic are analyzed via numerical experiments.The numerical results show that the departure capacity is negatively affected by the train departure control manner. In addition,(i) the real-time signal control can offer a higher train service frequency;(ii) the departure capacity gradually rises with the decrease in the line design speed to a limited extent;(iii) the departure capacity decreases with extension in the train length;(iv) the number of departed trains decreases as the train stop time increases;(v) the departure capacity is not affected by the section length. However, the longer the length, the worse the service quality of the urban rail transit line.The experiments show that the proposed cellular automaton model can be used to analyze the train service capacity of an urban rail transit system by performing quantitative analysis under various considered factors, conditions, and management modes.     

Properties of train traffic flow in a moving block system

The development direction of railways is toward the improvement of capacity and service quality, where the service quality includes safety, schedule, high speed, and comfort. In light of the existing cellular automaton models, in this paper, we develop a model to analyze the mixed running processes of trains with maximal speeds of 500 km/h and 350 km/h respectively in the moving block system. In the proposed model, we establish some sound rules to control the running processes of a train, where the rules include the departure rules in the intermediate stations, the overtaking rules, and the conditions of speed limitation for a train stopping at a station or passing through a station. With the consideration of the mixed ratio and the distance between two adjacent stations, the properties of the train traffic flow (including capacity and average speed) are simulated. The numerical results show that the interactions among different trains will affect the capacity, and a proper increase of the spatial distance between two adjacent stations can enhance the capacity and the average speed under the moving block.     

Station Model for Rail Transit System Using Cellular Automata

In this paper, we propose a new cellular automata model to simulate the railway traffic at station. Based on NaSch model, the proposed station model is composed of the main track and the siding track. Two different schemes for trains passing through station are considered. One is the scheme of ＂pass by the main track, start and stop by the siding track＂. The other is the scheme of ＂two tracks play the same role＂. We simulate the train movement using the proposed model and analyze the traffic flow at station. The simulation results demonstrate that the proposed cellular automata model can be successfully used for the simulations of railway traffic. Some characteristic behaviors of railway traffic flow can be reproduced. Moreover, the simulation values of the minimum headway are close to the theoretical values. This result demonstrates the dependability and availability of the proposed model.     

Analysis of the influence of occupation rate of public transit vehicles on mixing traffic flow in a two-lane system

Based on the existing classical cellular automaton model of traffic flow, a cellular automaton traffic model with different-maximum-speed vehicles mixed on a single lane is proposed, in which public transit and harbour-shaped bus stops are taken into consideration. Parameters such as length of cellular automaton, operation speed and random slow mechanism are re-demarcated. A harbour-shaped bus stop is set up and the vehicle changing lane regulation is changed. Through computer simulation, the influence of occupation rate of public transit vehicles on mixed traffic flow and traffic capacity is analysed. The results show that a public transport system can ease urban traffic congestion but creates new jams at the same time, and that the influence of occupation rate of public transit vehicles on traffic capacity is considerable. To develop urban traffic, attention should be paid to the occupation rate of public transit vehicles and traffic development in a haphazard way should be strictly avoided.     

固定闭塞系统下列车运行限速区段交通流特性分析

针对铁路交通中四显示固定自动闭塞系统下的限速区段，建立了元胞自动机模型，对限速区段的交通流进行了模拟，分析了限速区段长度、发车时间间隔和限速值对交通流的影响，模拟结果表明减少限速区段长度、适当增加发车时间间隔和提高限速区段限速值都可增加列车在绿灯下的运行时间. 关键词： 四显示固定自动闭塞 元胞自动机 交通流     

Scheduling trains on railway network using random walk method

According to random walk, in this paper, we propose a new traffic model for scheduling trains on a railway network. In the proposed method, using some iteration rules for walkers, the departure and the arrival times of trains at each station are determined. We test the proposed method on an assumed railway network. The numerical simulations and the analytical results demonstrate that the proposed method provides an effective tool for scheduling trains. Some characteristic behaviours of train movement can be reproduced, such as train delay.     

移动闭塞条件下线路弯道对列车交通流影响的研究

在NaSch模型的基础上,针对铁路线路特点提出了一种用于模拟铁路线路弯道的多列车追踪运行的元胞自动机模型.应用该模型,进行了计算机数值模拟,研究了具有不同弯道半径、不同外轨超高和不同弯道长度的线路弯道对铁路交通流的影响.模拟结果表明:建立的模型能够准确的反映出特殊线路交通流情况,线路弯道对列车的行车安全有较大的影响,同时再现了时走时停的交通波现象,根据仿真结果得出了随着弯道半径的增大,列车的晚点时间逐渐减少,合理选择弯道半径、外轨超高值和弯道长度,可以显著提高线路的通行能力,减低轮轨磨耗,保证列车的安全、舒适运行.所得结果对铁路线路选线设计和运营管理有一定的指导意义.     

An Improved Discrete-Time Model for Heterogeneous High-Speed Train Traffic Flow

This paper aims to present a simulation model for heterogeneous high-speed train traffic Row based on an improved discrete-time model(IDTM).In the proposed simulation model,four train control strategies,including departing strategy,traveling strategy,braking strategy,overtaking strategy,are well defined to optimize train movements.Based on the proposed simulation model,some characteristics of train traffic Bow are investigated.Numerical results indicate that the departure time intervals,the station dwell time,the section length,and the ratio of fast trains have different influence on traffic capacity and train average velocity.The results can provide some theoretical support for the strategy making of railway departments.     

Empirical analysis of dependence between stations in Chinese railway network

A railway transportation system can be represented by a bipartite network consisting of trains and stations, where a train is connected to all stations where it stops. In this paper, motivated by the resource-allocation process taking place on networks, we design a method to project a Chinese train-station bipartite network into a weighted station network. A new metric is proposed to quantify the dependence between pairs of stations, which is shown to follow a shifted power-law distribution. In addition, we compare the resource-allocation method and the well-known multiple-edge method, and the results indicate that our proposed method is more reasonable.     

Traffic dynamics of an on-ramp system with a cellular automaton model

This paper uses the cellular automaton model to study the dynamics of traffic flow around an on-ramp with an acceleration lane. It adopts a parameter, which can reflect different lane-changing behaviour, to represent the diversity of driving behaviour. The refined cellular automaton model is used to describe the lower acceleration rate of a vehicle. The phase diagram and the capacity of the on-ramp system are investigated. The simulation results show that in the single cell model, the capacity of the on-ramp system will stay at the highest flow of a one lane system when the driver is moderate and careful; it will be reduced when the driver is aggressive. In the refined cellular automaton model, the capacity is always reduced even when the driver is careful. It proposes that the capacity drop of the on-ramp system is caused by aggressive lane-changing behaviour and lower acceleration rate.     

Delay times in a cellular traffic flow model for road sections with periodic outflow

A simple cellular automaton to model traffic flow is used to analyze the impact of traffic lights on travel times. The model is investigated on a stretch of road with open boundaries, where the inflow is driven stochastically, but the outflow is controlled by a traffic light with periodically changing outflow rates. Especially in the transition regime from free flow to oversaturated flow, the detailed space-time structure can be used to derive analytical lower and upper boundaries for the travel time function. The analytical results have been verified by a simulation study. The function displays a strong non-trivial dependency on the length of the system, which is at odds with a well-known formula derived almost 50 years ago by Webster. Such a model is interesting both from a theoretical point of view and for applications.     

An improved cellular automaton model with the consideration of a multi-point tollbooth

Based on the classical Nagel–Schreckenberg model, we in this paper propose an improved cellular automaton (CA) model to study the influences of a multi-point tollbooth on traffic flow. The numerical results show that the multi-point tollbooth can be looked at as a bottleneck and that it can improve the road capacity compared with other tolling stations, which shows that the proposed model is more effective than other traffic flow models. In addition, the results can help readers to better understand the effects of a multi-point tollbooth on traffic flow and help traffic engineers to reasonably design the tolling station.     

Topological relation of layered complex networks

We present analytically the relation functions between degrees or clustering coefficients of a common station in both space L layer and space P layer of transportation systems. A good agreement between the analytical results and the empirical investigations in a railway system and three bus systems in China is observed.