Modern Physics Letters B
Vol.28,No.8(2014)1450060(11pages)
c Worl
d Scienti?c Publishing Company
DOI:10.1142/S0217984914500602
Analysis of train movement dynamics under various temporal–spatial constraints in?xed-block railway network
using extended cellular automaton model
Yonghua Zhou?,Zhenlin Zhang and Deng Liu
School of Electronic and Information Engineering,
Beijing Jiaotong University,Beijing100044,China
?yhzhou@https://www.doczj.com/doc/9b11571339.html,
Received11November2013
Revised23January2014
Accepted11February2014
Published12March2014
In the?xed-block railway tra?c,the trains adjust their speeds in view of their pre-
ceding allowable spaces caused by their respective front adjacent trains or speci?ed by
scheduling commands.The railway lines have the line-type speed limits within some
block sections and the point-type ones at the terminals of block sections.Those speed
limits originate from line conditions,scheduling commands and indications of signal
equipment.This paper attempts to in detail reveal the train movement mechanism syn-
thetically considering those temporal–spatial constraints.The proposed train movement
model de?nes four kinds of target points and utilizes them to successively engender the
instantaneous target points with their corresponding target speeds.It adopts the rule-
based description mechanism in cellular automata(CA)but with continuous spaces to
replicate restrictive,autonomous and synergistic behaviors of and among trains.The
selections of accelerations and decelerations are based upon the data models of practical
acceleration and deceleration processes;thereupon,the model is data-driven.The anal-
ysis of train movement dynamics through case studies demonstrates that the extended
CA model can reproduce the train movement mechanism of grading speed control to
satisfy the aforementioned temporal–spatial constraints.The model is applicable to rep-
resent the as-is or should-be states of train movements when adjustable parameters are
properly con?gured.
Keywords:Train movement modeling;temporal–spatial dynamics;?xed-block signaling;
cellular automaton;data-driven model.
1.Introduction
The restrictive,autonomous and synergistic behaviors of moving entities commonly exist in physical systems such as natural gas and liquid?ows,planet movements,and road and railway vehicle movements.The restriction re?ects that the movements of one entity are restricted by those of other entities or external temporal–spatial constraints.The autonomy stands for adjustment behaviors.The synergy is the
Y.Zhou,Z.Zhang&D.Liu
balancing or stable objective of the movements of entities.In the railway network, train movements are restricted by other trains,railway line conditions,and speci?ed scheduling commands.Each train interacts with its adjacent ones,and automati-cally adjusts its speeds through a set of control rules such that synergistic headways can be achieved.
Train movement models play a very important role in the control and man-agement of railway systems.They can be utilized for the performance evaluation of train operation plans.In case of real-time applications,the relatively accurate models of train movements facilitate predicting the potential operation con?icts either for the trains running in the same direction or toward the same convergent junction.In addition,they are employed to forecast the instants that trains will ar-rive at stations for travelers.Especially,they can act as auxiliary tools for the fault diagnosis of signaling equipment because they also indicate the application states of signaling equipment.Train movement models oriented toward train control are in-dispensable for the model-based controllers.The models,replicating realistic train movements are called as-is ones.While,the models,pointing out the should-be movement tendency are called should-be ones,which can be utilized for the trajec-tory con?guration of train operations for the advanced locomotive-mounted control equipment in the automatic train protection(ATP)or automatic train operation (ATO).1The modeling and simulation of railway tra?c have been applied to repre-sent speed adjustments and adequate headway maintenances of trains,2analyze the performances such as delay and capacity in the complex railway network,3realize intelligent decisions on train wait policies for delay management,4improve opera-tion e?ciency and safety,5and plan intermodal transportation connected by rail corridors.6
Cellular automata(CAs)are one type of modeling tool using discrete time and space to reproduce the dynamics of complex systems and behaviors,such as bi-ological7,8and physical9,10systems,road11,12and railway13,14tra?c,and escape and panic dynamics.15Microscopic tra?c simulation is e?ective at capturing tra?c patterns.16The CA models for microscopic tra?c simulation possess simple and sketchy merits at describing stochastic driving behaviors,which have been utilized to analyze tra?c?ow properties,17car accidents,18tra?c jams,19emergency ve-hicle movement,20and highway tra?c.21The CA models for railway tra?c were presented to replicate the dynamics of train movements in the moving-and?xed-block systems.13,14Various improved models were proposed to describe train move-ments in moving-like systems,22represent driving reactions and time headways23 reveal speed update mechanism with speed limits,24describe train-following move-ments,25represent train movements at stations,26and analyze carrying capacity.27 The scheduled target points were introduced into and two-steps of speed update mechanism were integrated in the improved CA model to capture restrictive,au-tonomous and synergistic behaviors of train movements.28–30The current CA mod-els for railway tra?c are deterministic,while those for road tra?c demonstrate a certain degree of stochastic characteristics.
Analysis of train movement dynamics under various temporal–spatial constraints In the?xed-block railway system,there mainly exist two kinds of speed control modes,i.e.grading control and one-time continuous control.The grading control is mainly used in low-and medium-speed trains,and the one-time continuous con-trol is primarily applied to high-speed trains.This paper attempts to reveal the train movement mechanism and dynamics of grading speed control under various temporal–spatial constraints utilizing the extended CA model which de?nes four kinds of target points and utilizes continuously variable accelerations and decelera-tions,and testify the applicability of the model for grading speed control of trains. The simulation of train movements based on the statistic data of practical acceler-ation and deceleration processes makes the results potential to tally with practical cases.
2.Train Movement Model
2.1.Speed limits
In the?xed-block railway network,there exist various kinds of speed limits.The ?rst kind is the speed limits on railway lines related to track conditions such as adhesion coe?cients,curvatures and gradients.The second one is the temporary speed restrictions which are speci?ed by scheduling commands due to unexpected events or maintenance works.The third one is the speed limits determined by train operation modes which designate the allowable maximum operation speeds to trains.These three kinds of speed limits can engender the most restrictive speed pro?les(MRSPs)which adopt the minimum value of all types of speed limits along railway lines.It is piecewise horizontal,but with abruptly changing points of speeds. In addition,the signal speed limits are very essential for train operations.On the one hand,they specify the speeds the trains should approach at the endpoints of block sections,denoted by the colors of signal lamps or the codes of track circuits.And on the other hand,they also denote the upper speed limits within block sections which should be incorporated into the MRSP,in total denoted as v lim(x)where x is the position along a railway line.The line-and point-type speed limits manipulate trains to generate dynamic speed limit curves.
2.2.Target points
In view of the complexities of speed limits for the?xed-block system,we de?ne four kinds of target points to distinctly reveal the movement mechanism of trains under grading speed control:
(i)p a:the start point of the block section that the front adjacent train is oc-
cupying,which can be detected utilizing the signaling equipment.The speed limit v a at that point is generally set to be0because p a is regarded at current instant as the instantaneous stop point to guarantee safety.If there is no train between the current train and its next dwelling station,the station is regarded as the front adjacent train.
Y.Zhou,Z.Zhang&D.Liu
(ii)p b:the end point of the block section currently occupied by the train,where the speed v b is determined by the colors of signal lamps or the codes of track circuits.
(iii)p b1:the preceding next abrupt speed-changing point in the v lim(x)where the speed v b1is the minimum value of all the speeds at that point.
(iv)p c:the running endpoint of a train temporarily speci?ed by the scheduling command where the speed limit v c is designated to be0.
De?ne d a,d b,d b1and d c are the distances from the current train to the above four kinds of target points,respectively.If the scheduling command is active, LC(sc)=1,or LC(sc)=0,where LC means life cycle.The allowable instanta-neous movement distance is determined by
d m=min(d a,d c)·LC(sc)+d a·(1?LC(sc)).(1)
In view of the current instant,the distance of the train from its current position to the nearest instantaneous target point p t is de?ned as
d t=min(d a,d b,d b1,d c)·LC(sc)+min(d a,d b,d b1)·(1?LC(sc)).(2)
On the speed–distance braking curve of train movements,let the points with the speeds equal to v a,v b,v b1and v c locate at p a,p b,p b1and p c,respectively. Consequently,the four braking curves will be generated,denoted as f a(x),f b(x), f b1(x)and f c(x)where x is the position coordinate with regard to the moving train. The instantaneous target speed v t at p t will be determined by
v t=min(v lim(x t),f a(x t),f b(x t),f b1(x t),f c(x t),v max)·LC(sc)
+min(v lim(x t),f a(x t),f b(x t),f b1(x t),v max)·(1?LC(sc)),(3) where x t is the position of p t and v max is the potential maximum speed of the train.
2.3.Model
De?ne x n and v n are the position and speed of a train at instant n,respectively;a n and b n are the acceleration and the deceleration of a train at instant n,respectively;
d r is th
e instantaneous reference distance for deceleration which is represented as d r=d s+v n,where d s is the braking distance from v n to v t according to the braking curve.The model is described as follows,29but the calculation approaches o
f d r and v t is di?erent from those in Ref.29.The dimensions of position and time in all the variables of the model such as a n,b n,v n,v t and so on are user-de?ned units,and the time interval between instants n and n+1are user-de?ned unit time.
(1)Speed update
IF v n>v lim(x n),v n+1=max(v n?b n,0)
ELSEIF v n=v lim(x n)AND d t≥d r,v n+1=v n
ELSE
IF d t>d r,v n+1=min(v n+a n,v max)
Analysis of train movement dynamics under various temporal–spatial constraints
ELSEIF d t=d r,v n+1=v n
ELSE
IF v n=v t=0,v n+1=v n
ELSE v n+1=min(max(v n?b n,v t),d m)
ENDIF
ENDIF
ENDIF
(2)Position update
x n+1=x n+v n+1.
The speed update mechanism involves two important steps which exist in the realistic train movements.The?rst step is to judge whether the current speed v n exceeds the v lim(x n)or not for the driver or mainly for the control equipment in the locomotive.If it exceeds,according to the di?erence degree between v n and v lim(x n), the corresponding braking measure will be adopted such as service or emergency braking with related deceleration b n.The second step is to enquire that if v n can be decelerated to v t at p t within d t at next instant n+1.If it holds,the train will have the opportunity to accelerate or hold the current speed.Otherwise,the train will decelerate.The model describes one kind of feedback adjustment mechanism for speed update and safe headway maintenance.Through the dynamically segmented tracks,various speed and space constraints are satis?ed,which will be shown in the following case studies.
3.Analysis of Train Movement Dynamics
3.1.Simulation conditions
The simulated railway network is shown in Fig.1.The network has?ve stations, i.e.A,B,C,D and E.There exist two transport lines,i.e.lines1and2,in the network.The route for line1passes A,F,C,G and E,while the route for line2 goes through B,F,C,G and D.F and G are the junctions for the two lines.One platform is employed at stations A and E for line1,and one platform is utilized at stations B and D for line2.Two platforms at station C are commonly used for the trains on lines1and2.The track segments AF,BF,FC,CG,GD and GE are composed of10,10,15,15,10and10block sections.The length of each block section is1km.The trains run according to the?xed-block operation mechanism
Fig.1.Railway network.
Y.Zhou,Z.Zhang&D.Liu
a b
Fig. 2.Acceleration and deceleration laws of a medium-speed train.(a)Acceleration and (b)deceleration.
where the maximum operation speeds of trains along lines1and2are con?gured
as v max
1=160km/h and v max
2=120km/h,respectively.The speed limits for the green,green–yellow,yellow and red signals are v g=160,v gy=120,v y=90 and v r=0km/h,respectively.The adopted acceleration and deceleration laws are displayed in Fig.2,which is hard to be described in an analytical formula because of the complexities of acceleration and deceleration processes.The dwell time at each station is T d=120s for lines1and2.The speed limits v o within the three block sections left to and one block section right to the junctions F and G,respectively, are set to be45km/h.The simulation step(unit time)is1s,and the maximal simulation time is3600s.Lines1and2dispatch trains every360s.The trains of line1are numbered as101,102,...,110,respectively,according to the dispatching order.Similarly,the trains of line2are orderly numbered as201,202, (210)
respectively.
3.2.d a,d b and d b1controls
We?rst test the model in case of existing signal and line speed limits,but without scheduling commands.In this case,we let the?rst train101of line1depart at instant0s and the?rst one201of line2depart at instant90s with the depar-ture interval360s for the remaining trains of both lines,to observe the moderate interaction behaviors between trains of lines1and2.Figure3demonstrates the position–time and speed–position–time diagrams of the trains of both lines on line1. The curves starting from the position of0km describe the movements of trains
a b
Fig.3.(Color online)Temporal–spatial dynamics of train movements on line1.(a)Position versus time and(b)speed versus position and time.
Analysis of train movement dynamics under various temporal–spatial constraints
a b
c d
e f
Fig.4.(Color online)The mechanism of speed update.(a)–(d)are for d a and d m,d b,d b1and d t,respectively.(e)Speed versus time and(f)speed versus position.
belonging to line1.The curves starting from the position of10km represent the movements of trains belonging to line2projected onto the line1.The acceleration, speed holding and deceleration phenomena can be observed in Fig.3.The speed limits can be achieved utilizing the proposed model on the railway line near to the junctions F and G.
We set the second train102of line1as an example to explain the speed update mechanism which is,thoroughly,shown in Fig.4.From Fig.3(a),we can learn that,before the junction F and after the junction G,train101of line1is the preceding adjacent one of train102.Between the junctions F and G,train201 of line2becomes the preceding adjacent one of train102.In addition,if there is no train between the current train and a station,the station will be regarded as the preceding adjacent train.Based upon these viewpoints,Fig.4(a)plots the variation process of d a.If there exists no scheduling command,d a=d m according to Eq.(1).At some instants,d a and d m have one-block-section abrupt ascents,which is because the front adjacent one of train102has just released its occupying block section.Figure4(b)shows the position variations with regard to the endpoint of the occupied block section.The gradients of the curves of position variations re?ect the speeds of train movements as shown in Fig.4(e).Figure4(c)illustrates the
Y.Zhou,Z.Zhang&D.Liu
a
b
Fig.5.(Color online)The mechanism of speed update from time1640s to1840s.(a)d a and d m versus time,(b)speed versus time.
distance variations of train102to the next abrupt speed-changing points in the v lim(x).The speed limits on lines1and2are con?gured at the positions of8to11, 25,38to41,and50km as45,0,45and0km/h,respectively,which can be found out in Fig.4(f).Therefore,the initial distances to the next abrupt speed-changing points in the v lim(x)are8,3,14,13,3,and9km,respectively,as shown in Fig.4(c). Because the line speed limit is con?gured in the unit of one block section,it is no wonder d t=d b,as represented in Fig.4(d).But,it should be noted that v t=v b. Figures4(e)and4(f)are the speed–time and speed–position plots,respectively.
We further elucidate the speed?uctuations using Fig.5,partial of Figs.4(a) and4(e).In Fig.5,the points A–O are marked to indirectly denote the critical positions that the train locates at,using d a s and d m s.Considering the braking reference distance d r from v g=160km/h toward v gy=120km/h,at point A, the train begins to decelerate.However,at point B,the preceding adjacent train is releasing its occupying block section and ready to enter the next one,which will lead to the increase of one block section for d a and d m.Consequently,the train gains the chance to accelerate from its current speed toward v g.The similar analysis can be undertaken for the speed?uctuations with regard to the points C,D and E. At point F,the train reaches the speed v gy,and considering the braking reference distance d r,continues to hold this speed for a while.G and H are the points for the train to accelerate from and decelerate toward v gy,respectively.At point I, the train again reaches the speed v gy,and continues to remain this speed until encountering the braking point J where it decelerates from v gy to v y=90km/h. At point K,the train reaches the speed v y.At point L,it begins to decelerate from v y to v o=45km/h.During this process,because of one-block-section ascent of d a and d m,the train will accelerate for a while until point N.Eventually,at point O, the train achieves the speed v o.It should be noted that from point L to O,the
Analysis of train movement dynamics under various temporal–spatial constraints operation objective of the train is to decelerate from v y to v o at point O rather than v r=0.
3.3.d a,d b,d b1and d c controls
In this section,we test the model when there exist signal and line speed limits, and scheduling commands.In order to observe the phenomenon of abrupt speed fall,the?rst train101of line1departs at41s,however,the?rst one201of line 2departs at0s.The departure intervals for the trains of lines1and2are still 360s.In this case,if there are no scheduling commands,the abrupt speed falls of trains101,102,...,110will be brought about by the trains201,202, (210)
respectively.Figure6illustrates the speed update mechanism of train102from instant660s to1080s with and without scheduling commands,utilizing the solid
a b
c d
e f
g h
Fig.6.(Color online)The mechanism of speed update with and without scheduling commands.
(a)–(f)are for d a,d b,d b1,d c,d m and d t,respectively.(g)Speed versus time and(h)speed versus position.
Y.Zhou,Z.Zhang&D.Liu
and broken lines,respectively.Figures6(g)and6(h)display the speed update with time and position,respectively.The abrupt speed descent will happen to train102 if there is no scheduling command as shown in Figs.6(g)and6(h).However,as depicted in Fig.6(d),if the scheduling command is issued before the instant715s when the distance to the scheduled target point and the speed of train102just locate on the braking curve,the train can steadily approach the scheduled target point as displayed in Figs.6(g)and6(h).Comparing Figs.6(a)and6(d)with Fig.6(e),we can reach the conclusion that d m stands for the spatial constraint, and if the scheduling command is active with d c
4.Conclusion
In order to thoroughly consider various kinds of speed limits for grading speed control system,p b1is explicitly introduced into the CA model in Ref.29.p b1locates at the next abrupt speed-changing point in the v lim(x).Besides,we utilize the continuously variable accelerations and decelerations to describe train movements, which are based upon the historical data of train operations.Consequently,the braking reference distance d r is related to the current speed and the deceleration process.For the one-time continuous speed control,p b in this paper can be omitted, which is rede?ned in Ref.30.We have utilized the data model abstracted from the practical acceleration and deceleration processes to undertake case studies having mixed point-and line-type speed limits.The numerical results demonstrate that the extended CA model can replicate the train movement dynamics because of speed feedback adjustment,and represent the movement mechanism required by the grading speed train control,that is,trains should arrive at speci?ed positions with designated speeds.However,the practical train movements of grading speed control should?uctuate around this rational analysis.
Acknowledgments
This work is partially supported by the National Natural Science Foundation of China(Grant No.61074138)and the Fundamental Research Funds for the Central Universities of China(Grant No.2009JBM006).
Analysis of train movement dynamics under various temporal–spatial constraints
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图 2.4 新建工程向导第3页 这一步一般直接点击“Next”跳过，进入下一步，选择目标器件。在“Family”下拉列表中选择器件系列为Flex10K，在Target device选项中选中Specific device selected in ‘Available devices’list，依据实验平台的型号，确定器件型号Available device 为。 图 2.5 新建工程向导第4页
一平台功能简单介绍1 数据采集和传输 1、GIS地图 2、道路监控点位管理 3、中转服务器管理配置 4、实时监控 5、卡口数据库 6、黑名单库 7、套牌车库 8、车管库接入 9、违章库接入 10、盗抢库接入 11、犯罪人员库接入 2 数据分析挖掘 1、数据和视频查询 2、轨迹分析 3、轨迹跟踪 4、分析研判 5、视频图像处理 3联网布控报警 1、联网布控 2、实时报警 4调度指挥 1、GPS定位 2、围堵预案 3、短信平台 4、第三方系统联动接口 5资源共享 1、基础数据同步接口 2、第三方系统数据接口 3、时钟系统接口 6设备维护管理
1、系统巡检 2、设备状态管理 3、维护调度系统接口 4、系统运行日志 二业务应用场景 场景1： 某街道附近连续发生团伙案件，结合目击者报告，犯罪团伙乘坐一辆小型车进行犯罪，公安干警希望了解当时附近道路监控点的记录。 平台操作1： 在GIS地图上标注出几次发生案件的地点； 在GIS地图上标出以各犯罪地点为圆心，周边500米内的道路监控点； 从中选择嫌疑车辆可能经过的若干个卡口； 对各标出的道路监控点进行单独点击查询演示；（犯罪事件前后30分钟过车信息犯罪事件前后30分钟视频文件信息，道路监控点三维场景演示） 场景2： 公安干警希望得到几次犯罪时间在几个道路监控点的均出现的车辆信息，并结合各种线索缩小侦查范围。 平台操作2： 在GIS上选定的几个道路监控点进行联合查询，条件为几次犯罪时间前后，在其中任一个道路监控点出现过的车辆信息； 将得到的车辆信息列表分别和车管库，盗抢库，犯罪人员信息库相关联进行搜索，检查其中是否有车主是有前科人员，是否有车辆属于盗抢车辆，如果有，都属于嫌疑更大的目标； 根据以上查询缩小查询范围以后，得到10辆以下的车辆信息，对此批车辆进行轨迹分析，排除不可能的车辆，进一步缩小范围； 场景3： 公安干警对嫌疑车辆进行布控，设置围堵预案。 平台操作3： 对最终的3~5辆车，在GIS上进行布控操作； 在GIS上，对嫌疑车辆设置围堵预案； 场景4： 平台道路监控点发现嫌疑车辆，进行报警，公安干警根据设置的围堵预案在前方拦截，抓获嫌疑车辆。 平台操作3： 在GIS上弹出报警窗口和报警监控点位置，点击弹出报警信息和车辆图片； 在GIS上，根据报警监控点位置激发相应围堵预案，使用短信平台通知一线干警进行围堵； 在GIS上，根据GPS信息实时显示围堵警车的轨迹，根据各卡点信息显示嫌疑车辆
// Frame Panel Button Lable Checkbox import java.awt.Button; import java.awt.Checkbox; import java.awt.Frame; import java.awt.GridLayout; import https://www.doczj.com/doc/9b11571339.html,bel; import java.awt.event.ActionEvent; import java.awt.event.ActionListener; public class NewCheckbox { public static void main(String[] args) { Frame f = new Frame("Checkboss示例"); Button b = new Button(); b.setLabel("关闭"); b.addActionListener(new ActionListener() { public void actionPerformed(ActionEvent e) { System.exit(0); } }); f.setLayout(new GridLayout(2, 3)); Label lb = new Label("个人爱好");
Checkbox c1 = new Checkbox("读书"); Checkbox c2 = new Checkbox("打球"); Checkbox c3 = new Checkbox("上网"); Checkbox c4 = new Checkbox("看电视"); f.add(lb); f.add(c1); f.add(c2); f.add(b); f.add(c3); f.add(c4); f.setSize(400, 400); f.setVisible(true); } }