外文翻譯--模擬軌道交通列車運行的跟車模型研究

1、<p><b>　　中文4680字</b></p><p>　　畢業(yè)設(shè)計（論文）外文參考文獻及譯文</p><p>　　英文題目 SIMULATING TRAIN MOVEMENT IN RAILWAY </p><p>　　TRAFFIC USING A CAR-FOLLOWMING MODEL

2、 </p><p>　　中文題目 模擬軌道交通列車運行的跟車模型研究 </p><p><b>　　Abstract</b></p><p>　　Based on a car-following model, in this paper, we propose a new traffic model fo

3、r simulating train movement in railway traffic. In the proposed model, some realistic characteristics of train movement are considered, such as the distance headway and the safety stopping distance. Using the proposed tr

4、affic model, we analyse the space-time diagram of traffic model, the trajectory of train movement, etc. Simulation results demonstrate that the proposed model can be successfully used for simulating t</p><p>

5、;　　Keywords: Train movement, Railway traffic, Car-following model</p><p>　　1 Introduction</p><p>　　Train movement calculation is used to calculate the velocity and distance profile as a train tr

6、avels from one station to another. When the theoretical control algorithm of train movement is analysed and evaluated, a computer-based simulation model is necessary. An important problem is how to establish and solve th

7、is simulation model. Recently, a number of studies have been performed in this field. However, many characteristic behaviours of train movement remain unknown. What are the mechanisms b</p><p>　　The car-foll

8、owing model is one of the important traffic models in studying traffic model, and it is used mainly to describe the behaviour of an individual driver. Several car-following models have been proposed, including the early

9、car-following models, and some recent improved models. Since in the car-following model realistic driver behaviour and detailed vehicle characters are included, it can be used to simulate various traffic flows which are

10、observed in real traffic. In addition, by using </p><p>　　In 1995, Bando et alproposed an improved car-following model, which is called the optimal velocity model. Such an improved model attracts a lot of at

11、tention because of its distinctive features in representing real traffic flow. Lately, research has been carried out on extending the optimal velocity model. A well known extended model, called the “general optimal veloc

12、ity model”, was proposed by Nagatani in 1999 and Sawada in 2001 separately. But most of them focused on analyzing the characters of</p><p>　　In the present work, based on the optimal velocity car-following m

13、odel, we propose a new model for simulating train movement, where the influence of tracked trains is considered. Using the proposed simulation model, we study and discuss some characteristic behaviours of train movement

14、in railway traffic. To our knowledge, this work explicitly shows this effect for the car-following model for the frst time. The remainder of the present paper is organized as follows. In Section 2, we introduce the</p

15、><p>　　2 The optimal velocity model</p><p>　　The car-following model describes the motion of a vehicle following its leader vehicle without making a lane change. In the car-following model, a follo

16、wer vehicle tries to maintain a space gap behind its leader vehicle. A classical car-following model was proposed by Pipes. In order to account for the time lag, Chandler et al uggested an improved car-following model,&

17、lt;/p><p><b>　　(1)</b></p><p>　　Where is the position of vehicle n at time t, T is a response time lag, and o is the sensitive coefficient. For a more realistic description, Newell pr

18、esented the optimal velocity car-following model,</p><p><b>　　(2)</b></p><p>　　whereis called the optimal velocity function, and is the headway of vehicle n at time t. More than 30 y

19、ears later, Bando et al suggested a well-known optimal velocity model,</p><p><b>　　(3)</b></p><p>　　where is the relaxation time. </p><p>　　In the optimal velocity mode

20、l, the deceleration and the acceleration of the vehicle are described by a simple differential equation. According to such a differential equation, the behaviour of the driver is dependent mainly on the headway (the dist

21、ance between two successive vehicles). This means that the driver is assumed to be only looking at the leader vehicle. But, in more realistic situations, the driver considers more information about vehicles around him/h

22、er. Apart from this, the relaxat</p><p>　　In order to reproduce traffic as realistically as possible, some complex models are proposed, but they are at the cost of introducing a large number of parameters, o

23、r, losing their realistic features in the deterministic limit. For example, the “generalized-force model” with a generalized optimal velocity function was proposed in Ref. This model could successfully reproduce the time

24、-dependent gaps and velocities. However, the acceleration time and deceleration time in this model are still unreal</p><p>　　3 Principle of the train control system</p><p>　　The train control sy

25、stem plays a central role in railway traffic. Usually, it is used to decide how a driver operates under safety restrictions and other considered constraints. Two types of the train control systems have been developed, i.

26、e. the fixed-block system and the moving block system. The fixed-block system has been widely used in modern railway traffic for more than one century. However, as signaling technology is developed, the moving block syst

27、em becomes of considerable importance an</p><p>　　With the moving block system, electronic communications between the control centre and trains continuously control the trains, and make them maintain the saf

28、ety stopping distance. In a moving block equipped system, using the information about the velocities and the locations of all the trains in its area, controllers can optimize system performance and respond to events quic

29、kly and effectively. The advantages of the moving block system are that the line capacity can be increased and the traffic </p><p>　　In the moving block system, between two successive trains, the following t

30、rain needs to adjust its velocity continuously. If the distance between two successive trains is smaller than the safety stopping distance, the following train will be forced to brake to a lower velocity or stop at a sit

31、e on the track line. Several types of moving block systems have been developed, i.e. the moving space block, the moving time block and the pure moving block. In the present paper, we employ the moving space</p>&l

32、t;p>　　4 Our model</p><p>　　The behaviour of train movement in railway traffic differs from that of vehicle movement in road traffic. The deceleration and the acceleration of the train are limited to a ran

33、ge between -2 and 2. But such a range in road traffic is between -3 and 4.The velocity relaxation time is larger than that in city traffic and freeway traffic (realistic velocity relaxation time is of the order of 10 s i

34、n city traffic and 40 s in freeway traffic). In addition, the2202 Li Ke-Ping et al Vol. 18 safety stopp</p><p>　　The car-following model proposed in Ref. is a well-known optimal velocity model, where the opt

35、imal velocity function is taken as. Based on such a car-following model, we propose a new improved model for simulating train movement. The proposed model is as follows:</p><p><b>　　(4)</b></p

36、><p>　　In the above equation, we have introduced a function . This function ensures that the improved equation model meets the following two conditions: (i) the deceleration and the acceleration of the train ar

37、e limited to a given range; (ii) a crash can be avoided when the velocity relaxation time is of a high order. Here and are adjustable parameters. In simulation, we need to select reasonable values of and .</p>&

38、lt;p>　　The dynamic behaviour of train movement near a station is more complex. When train prepares to travel into a station, if the station in front of train n is occupied by other trains, train n must keep away from

39、 the station, otherwise, train can travel into the station directly. In the former case, train maintains a safety stopping distance from the train in front of it, but in the latter case, the safety stopping distance be

40、tween train and the station is neglected. In the former case, the opt</p><p>　　The boundary condition used in this paper is open. Considering a single track line with a length of L, the boundary condition i

41、s as follows: (i) when the section from site 1 to site is empty, a train with the velocity is created. This train immediately travels according to the equation model (4). Here the parameter is called the departure int

42、erval, and it must be larger than or equal to the safety stopping distance . (ii) At site L, trains simply move out of the system. In order to compare si</p><p>　　5 Simulation</p><p>　　We use th

43、e proposed model to simulate the train movement in single line railway traffic. The train control system employs the moving space block system. The dynamic equation of train movement is described by Eq. (4). The proposed

44、 equation model is suitable for computer programming. To start with, by changing the time derivative, the proposed equation modelis simplified into a discrete model. Then we iterate the discrete equation model under the

45、open boundary condition. The basic program is that </p><p>　　In simulation, a system with length L = 10000 is considered (L = 10000 units correspond to L =10000 m). The number of the iteration time steps is

46、Ts = 2000. One station is designed in the middle of the system, i.e. the station is at the site l = 5000. As a train arrives at a station, it needs to stop for a time (say, Td) and then leaves the station. Td is called t

47、he station dwell time. The values of and are related mainly to the maximum velocity . When is larger, and should take smaller value</p><p>　　Simulation results demonstrate that when the departure interval

48、 is large, trains can travel without any disturbance, and when the departure interval is small, train delays begin to emerge. In order to study the characteristic behaviour of train movement, we investigate the space-t

49、ime diagram of the railway traffic flow. Figure 1 shows part of the space-time diagram of railway traffic flow for = 40. Here we plot 10000 sites in 1000 consecutive time steps. The horizontal direction indicates the<

50、;/p><p>　　In the present paper, we focus on the case where the departure interval is small. Under such a condition, we can observe how trains change their velocities, and maintain the safety stopping distance b

51、etween them. In Fig.1(b), all trains start from the departure site, i.e. the site = 1, and then arrive at the station, i.e. the middle site = 5000. After the station dwell time , they leave the station. When they arrive

52、at the arrival site, i.e. the site = 10000, they leave the system immediately. B</p><p>　　As mentioned in Section 4, when a train travels from one station to another, its deceleration and acceleration are li

53、mited to a range between -2 and 2 . Using the proposed model, the deceleration and acceleration of trains can be made to enter into such a given range by controlling the values of c1 and c2. The relevant results are pres

54、ented in Fig. 3. Here we record the decelerations and accelerations of all trains at all times. The parameters , and are the same as those used in Fig.1. From Fi</p><p>　　In reality railway traffic, one of

55、 the important factors which factors train movement is the safety stopping distance. With the moving block system, the safety stopping distance between two successive trains must be maintained. For example, when the dist

56、ance between two successive trains is smaller than the safety stopping distance, the following train must decelerate. In order to further test the proposed model, we measure the distribution of the distance headway at a

57、 given time, where ¢si is </p><p>　　6 Conclusions</p><p>　　We proposed an improved car-following model for simulating the train movement in railway traffic. By iterating the proposed equati

58、on model, we simulate the train movement under the moving block system condition. The numerical simulation results indicate that the proposed model can describe well the train movement in railway traffic. Not only can th

59、e dynamic behaviour of train movement be described, but also some complex phenomena observed in real railway traffic, such as the train delays, can be</p><p>　　In a practical train control system, train move

60、ment is restricted by several factors, such as the track geometry, traction equipment, train length, etc. In the proposed model, some factors have not been considered, thereby leading to the simplification of the train m

61、ovement calculation. Although the proposed model is simplified, it can reproduce some characteristic behaviours of train movement, moreover it provides a new approach for the further analysis and evaluation of train cont

62、rol systems.</p><p><b>　　摘 要</b></p><p>　　根據(jù)跟車模型，在本文中，我們提出了在鐵路交通模擬列車運行一個新的交通模式。在所提出的模型，火車運動的一些現(xiàn)實的特征可以被描述，如距離上前和安全制動距離。利用所提出的流量模型，我們分析流量模型的時空圖，列車運行等的彈道仿真結(jié)果表明，該模型可以成功地用于模擬列車運行。一些復(fù)雜的

63、現(xiàn)象可被再現(xiàn)，如復(fù)雜的列車加速、減速和列車延遲傳播。</p><p>　　關(guān)鍵詞：列車運行；鐵路交通；跟馳模型</p><p><b>　　1 引言</b></p><p>　　列車移動計算用于計算一列火車從一個站到另一個速度和距離。對列車運動理論控制算法進行分析和評價后，我們得出了基于計算機的仿真模型是非常有必要的。我們面臨的一個重要的問題就

64、是如何建立和運用這個仿真模型。最近，我們在這一領(lǐng)域已經(jīng)進行了大量的研究，然而，列車運行的許多特征在仿真模型上仍存在很多問題。例如列車晚點出現(xiàn)的原因是什么？追蹤的列車之間是怎樣相互影響的？</p><p>　　跟車模型是研究交通模型的重要交通模型之一，它主要是用來顯示駕駛員駕駛和操作的行為?，F(xiàn)在已經(jīng)有幾個跟車模型已經(jīng)被提出，其中包括早期的跟車模型和最近的一些改進型號。由于跟車模型逼真的駕駛和車輛的詳細信息都包括在內(nèi)

65、，它可以被用來模擬列車在實際運行中的變化。除了列車運行不同的變化，通過利用跟車模型，可以對一些模擬產(chǎn)生的結(jié)果進行推導(dǎo)和解析。</p><p>　　1995年，坂東等人提出了一種改進的跟車模型，這就是所謂的最優(yōu)速度模型。這種改進后的模型吸引了眾多研究人員，因為它對實際交通流的鮮明特點做了大量研究。最近，研究已經(jīng)進行了擴展的最優(yōu)速度模型。提出了由永谷在1999年的提出的一個眾所周知的擴展模型，稱為“一般最優(yōu)速度模型”

66、。但大多集中在從物理學(xué)的觀點分析密度波的特點。</p><p>　　在目前的工作中，基于最優(yōu)速度跟馳模型，我們提出了模擬列車運行，其中跟蹤列車的模式被認為是一種新的模式。利用所提出的仿真模型，我們探討和研究了軌道交通列車運行的一些實際的特征行為。據(jù)我們所知，這項工作明確地顯示了這種效應(yīng)的跟車模型的時間。本文件的其余部分安排如下。在第2節(jié)中，我們介紹了最優(yōu)速度模型。列車控制系統(tǒng)的工作原理在第3節(jié)的介紹。在第4節(jié)中，

67、我們列出了該模型。數(shù)值和分析結(jié)果示于第5節(jié)，最后，通過使用這種方法得到的結(jié)論并在第6節(jié)中介紹。</p><p><b>　　2 優(yōu)化速度模型</b></p><p>　　跟車模型描述未做變更車道以前的車輛的運動。在跟車模型，一個跟隨車輛試圖保持其前方者車輛的空間差距。提出通過管道一個經(jīng)典的跟車模型。為了解釋的時間滯后，錢德勒等人提出一種改進的跟車模型，</p&g

68、t;<p><b>　　(1)</b></p><p>　　其中，xn(t)為車輛n在時間t的位置，T是一個響應(yīng)時間滯后，o是靈敏系數(shù)。對于一個更現(xiàn)實的描述，紐維爾提出的最優(yōu)速度跟馳模型，</p><p><b>　　(2)</b></p><p>　　其中稱為最優(yōu)速度函數(shù)， </p><

69、p>　　為車輛的n在時間t的進展。</p><p>　　超過30年后，坂東等人提出了一個著名的最優(yōu)速度模型，</p><p><b>　　(3)</b></p><p><b>　　其中是松弛時間。</b></p><p>　　在最佳的速度模型中，車輛的加速度是由一個簡單的差分方程來描述。根據(jù)

70、這樣的微分方程，駕駛員的行為依賴于列車間距（兩個連續(xù)的車輛之間的距離）。這意味著駕駛員被假定為只著眼于領(lǐng)先車輛。但是，在更現(xiàn)實的情況下，駕駛員認為對周圍其他車輛的詳細信息也要有所了解。此外，松弛時間在方程(3)是一個重要的參數(shù)，它必須被合理地選擇，以保證兩個連續(xù)的車輛之間的不會碰撞。</p><p>　　為了盡可能再現(xiàn)交通實際現(xiàn)象，提出了一些復(fù)雜的模型，他們引進了大量的參數(shù)，或者，在失去確定性前提下限制他們在現(xiàn)實

71、功能的成本。例如，提出了“廣義模型”具有廣義最優(yōu)速度函數(shù)在文獻。這個模型可以成功地再現(xiàn)相關(guān)的時間間隔和速度。然而，加速時間和減速時間在這個模型仍然是無限小。因此，我們做出了很大的努力來改善最優(yōu)速度跟馳模型，并使其適用于模擬各種真實的列車運行。</p><p>　　3 列車控制系統(tǒng)原理</p><p>　　在列車控制系統(tǒng)中起著鐵路交通中心作用。通常，它是用來決定列車運行安全和操作的。兩種類型

72、的列車控制系統(tǒng)已經(jīng)被開發(fā)出來，即固定塊系統(tǒng)和移動塊的系統(tǒng)。固定塊系統(tǒng)已廣泛應(yīng)用于現(xiàn)代鐵路交通已有一個多世紀。然而，由于通信技術(shù)發(fā)達，移動閉塞系統(tǒng)變得相當?shù)闹匾⒃谀骋惶炜赡軙〈潭ㄩ]塞系統(tǒng)。</p><p>　　隨著移動閉塞系統(tǒng)的發(fā)展，控制中心和列車之間的電子通信可以連續(xù)控制列車運行，并讓兩列相鄰列車保持安全的制動距離。在移動閉塞系統(tǒng)配備使用有關(guān)列車速度和所有列車的位置在其區(qū)域中的信息，控制器可以優(yōu)化系統(tǒng)性能

73、并對事件迅速和有效的反應(yīng)。移動塊系統(tǒng)的優(yōu)點是，線路的列車運行密度可以增加，交通流動性和能量效率可以得到改善。</p><p>　　在移動閉塞系統(tǒng)，兩個連續(xù)的列車之間需要不斷調(diào)整其速度。如果兩個連續(xù)列之間的距離小于安全制動距離越小，后面的列車將被迫制動到較低的速度或停止在一個站點上的軌跡線。幾種類型的移動閉塞系統(tǒng)已經(jīng)被研究出來，即運動空間塊，移動時間塊和純移動塊。在本文中，我們采用了移動空間模塊作為研究塊系統(tǒng)。有些

74、方法可以很容易地擴展到其他塊的系統(tǒng)。</p><p><b>　　4 我們的研究模型</b></p><p>　　鐵路運輸中列車的運行現(xiàn)象不同于在道路交通車輛的運動。列車的加速度限制為-2和2之間的范圍內(nèi)。道路交通加速度的限制為-3和4之間的范圍內(nèi)。列車的速度弛豫時間大于城市交通和高速公路交通(現(xiàn)實的列車速度弛豫時間為10秒而在城市交通和高速公路交通弛豫時間為40秒)

75、。最大速度和列車的減速率和安全制動距離是密切相關(guān)的。通常，該安全制動距離被定義為，其中s被稱為安全邊距，是火車最大速度，b是列車的減速率。為了使用的跟車模型來模擬軌道交通列車運行，我們在這里提高了優(yōu)化速度模型，并使其適合于描述軌道交通列車運行。</p><p>　　這里提出的跟車模型是一個眾所周知的最優(yōu)速度模型，其中最優(yōu)速度函數(shù)為?；谶@樣的跟車模型，我們提出了模擬列車運行一個新的改進型號。該模型如下所示： &l

76、t;/p><p><b>　?。?） </b></p><p>　　在上述公式中，我們引入了函數(shù)，此函數(shù)確保了改進的方程滿足下列兩個條件：(i)列車在減速和加速被限制在一個給定的范圍內(nèi); (ii)可避免系統(tǒng)崩潰時速度弛豫時間是一個高位。這里和是可調(diào)節(jié)的參數(shù)。在模擬中，我們需要合理的選擇和的值。</p><p>　　車站附近列車運行的動態(tài)行為更為復(fù)雜

77、。當列車準備行駛到到一個站，如果列車前面的站被其他列車占用，列車必須停在車站以外。相反，火車可以直接行駛到該站。在前一種的情況下，列車必須要和它前面的列車保持安全制動距離，但在后面一種情況下，安全慢車與車站之間的距離可以忽略。在前面一種的情況下，最佳的速度函數(shù)為，而在后面一種的情況下，最佳的速度函數(shù)的火車n可以被簡化為。</p><p>　　在本文中使用的邊界條件是沒有太多約束的?？紤]一條為L的長度的單一軌道線，

78、邊界條件如下：(i)當從站點1到站點的部分為空，則創(chuàng)建與速度相關(guān)的列車運行。列車馬上根據(jù)方程模型記錄(4)。這里的參數(shù)被稱為出發(fā)間隔，并且它必須是大于或等于安全制動距離。(ii)在軌道線L，為了模擬結(jié)果與現(xiàn)場測量比較，一次迭代大致相當于1秒，并且一個單元的長度為約1μm。 </p><p><b>　　5 仿真</b></p><p>　　我們利用該模型來模擬單線鐵路

79、交通列車運行。列車控制系統(tǒng)采用了移動空間閉塞系統(tǒng)。列車運動的動力學(xué)方程由方程描述。建議的方程模型適用于計算機編程。首先，通過改變時間的導(dǎo)數(shù)，方程簡化成一個離散的模型。然后我們遍歷開放邊界條件下的離散方程模型。其基本程序是，在每個時間步，對所有列車中，我們使用當前的速度和列車的位置來計算他們的速度和位置在下一個時間步長。</p><p>　　在模擬中，與長度L = 10000的系統(tǒng)被認為是(L = 10000單位對

80、應(yīng)于L =萬米)。的迭代時間步數(shù)為Ts = 2000 ，其中一個站被設(shè)計在系統(tǒng)的中間，即該站是在現(xiàn)場升= 5000 。作為列車到達一個站時，需要停止一段時間 ，然后離開了車站。 Td被稱為站的停留時間。 和的值主要與最大速度 。當ν最大較大， 和應(yīng)采取較小的值。與此相反，當V最大越小， 和應(yīng)采取更大的值。對于給定的時，當越大，應(yīng)取較小的值，并且當為較小，應(yīng)該取較大的值。因為減速度b是變型中，安全制動距離也是一個變種。但是，在列車運行的過

81、程中，通常被認為是一個常數(shù)。所以的公式中設(shè)置在減速的中間值。速度弛豫時間和安全裕度間距分別被設(shè)定為 = 100和 = 10 ，經(jīng)過足夠的瞬態(tài)時間，我們開始記錄流量的數(shù)據(jù)。</p><p>　　仿真結(jié)果表明，當發(fā)車間隔為大，火車可以在沒有任何干擾的旅行，并在出發(fā)間隔小，列車晚點開始出現(xiàn)。為了研究列車運行的特征行為，我們探討了鐵路交通流的時空圖。圖1所示為=40鐵路交通流的時空圖的一部分，在這里我們畫出10000網(wǎng)站

82、在1000個連續(xù)的時間步長。水平方向指明了列車向前行駛的方向。垂直方向表示時間演化步驟。參數(shù)和分別設(shè)定為 =50和=0:001。在圖1中，列車的位置由圓點表示。從圖1中，我們可以發(fā)現(xiàn)，如圖1(a)所示，那里的磁通流量可以增加，減少的出發(fā)間隔Ls和圖1(b)所示的復(fù)雜的流量流，其中列車晚點向后移動。</p><p>　　在本文中，我們重點在哪里出發(fā)間隔小的情況。在這種條件下，我們可以觀察到列車如何改變其速度，并保持

83、它們之間的安全制動距離。在圖19( b)所示，所有列車從出發(fā)站點啟動，即現(xiàn)場升= 1，然后到達車站時，即中間位置 = 5000 ，經(jīng)過該站停留時間 ，他們離開車站。當他們在到達到達現(xiàn)場，即現(xiàn)場 = 10000 ，便立刻離開系統(tǒng)。車站前，列車晚點形成和傳播倒退。在列車晚點傳播倒退，其時間間隔停在賽道增加。這是列車運行的復(fù)雜動態(tài)行為發(fā)生在靠近車站。當一列火車經(jīng)過一站，它需要停下來讓乘客上落。在這個過程中，它需要加速和連續(xù)地減速。如果站停留時

84、間大，列車晚點可能形成和傳播倒退。圖2示出了局部空間，顯示附近的一個車站的列車的位置和速度。這里的數(shù)字表示列車的速度。 和的值被設(shè)定為 = 100和 = 0:001 。從圖2中，我們可以清楚地看到，作為序列C停在車站，列車ð就是后面直接序列C需要減速，然后停在站臺的列車E的前面隨著時間的推移，一些火車前C火車才顯示。這些結(jié)果表明，該模型能夠成功地捕獲軌道交通的預(yù)期延遲。</p><p>　　圖1 當出

85、發(fā)間隔距離很小時且 (a)= 2和= 10, (b)=</p><p>　　和= 20時的鐵路交通的局部空間-時間圖 </p><p>　　圖2 當= 15, =和= 100時列車速度和位置</p><p>　　正如在第4節(jié)中，當一列火車從一個站移動到另一個，它的減速和加速被限制為-2和2之間的范圍內(nèi)。利用所提出的模型，列車的減速度和加速度可通過控制和的值進入到這

86、樣一個給定的范圍內(nèi)。有關(guān)結(jié)果示于圖3，在這里，我們在任何時候都記錄所有列車的減速度和加速度。參數(shù)，和是相同于圖1中。從圖3中，我們可以看到，列車的加速度是在0和2之間的范圍內(nèi)，以及列車的減速度為-2和0之間的范圍內(nèi)。在一般情況下，和中的較高的值，較大的限制了減速和加速的范圍就越大。</p><p>　　在現(xiàn)實的鐵路交通，重要因素，其中因素列車運動之一，是安全的停止距離。與移動塊系統(tǒng)，必須保持連續(xù)兩個串之間的安全制

87、動距離。例如，當兩個連續(xù)列之間的距離小于安全制動距離越小，下列列車必須減速。為了進一步檢驗該模型，我們衡量在給定時間，其中是火車我訓(xùn)練的距離車頭間距分布¢ SI I + 1 。圖4顯示了車頭間距在時間t的分布= 1000 ，其中實線表示測量結(jié)果，而虛線表示安全制動距離。在圖4中，在時刻t = 1000年，有4列車行駛的單行。從圖4 ，很明顯，所有的測量結(jié)果是較安全的制動距離大。仿真結(jié)果表明，該模型是一種有效的工具，模擬列車運行

88、。</p><p>　　圖3 當 =和= 20時列車的加速度和減速度</p><p>　　圖4 當 = 40, =和= 20時的車頭間距分布</p><p><b>　　6 結(jié)論</b></p><p>　　我們提出了一個改進的跟馳模型用于模擬軌道交通列車運行。通過迭代建議方程模型，我們模擬了移動閉塞系統(tǒng)條件下的列車

89、運行。數(shù)值模擬結(jié)果表明，該模型能在軌道交通描述以及列車運行。不僅可以火車運動的動態(tài)運行進行描述，而且也可以再現(xiàn)一些實際的鐵路交通觀察到復(fù)雜的現(xiàn)象，如在列車晚點，可以重現(xiàn)。</p><p>　　在一個實際的列車控制系統(tǒng)，列車運動是由多種因素，如軌道幾何形狀，牽引設(shè)備，列車長度等，在有的模式中，一些因素沒有被考慮進去，從而導(dǎo)致的列車運動的簡化限制計算。雖然該模型得到簡化，它可以再現(xiàn)列車運行的一些行為特征，但是它提供的