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研究生:黃佳伶
研究生(外文):Chia-Ling Linda Huang
論文名稱:一維車流系統之動力學研究
論文名稱(外文):The Study of The Dynamics of The One-dimentional Traffic Flow
指導教授:李紀倫
指導教授(外文):Chi-Lun Lee
學位類別:碩士
校院名稱:國立中央大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
畢業學年度:98
語文別:英文
論文頁數:42
中文關鍵詞:壅塞顆粒狀系統塞車交通
外文關鍵詞:TrafficGranularJamming
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  • 收藏至我的研究室書目清單書目收藏:1
藉由『跟車模型』(car following model),我們探討一維車流系統的動力學行為。根據原模型,我們額外引入車距因素以及一防止超車的repulsive Lennard-Jones potential,以期使我們的模型更貼近真實系統。我們所控制的是週期性單線道高速公路。我們觀察其上壅塞發生的過程。此壅塞是由不明顯的車輛擾動所引起的。基本圖型(the fundamental diagram)在此篇論文中會被討論。
從我們的觀察中發現,當車流系統的密度高於某個門檻時,系統會趨向不穩定而容易造成壅塞。壅塞的形成過程可分為三階段: 一、堆疊與過塞;二、和緩;三、穩定存在。根據模擬的結果,當達成穩定態時,車輛會重複前車的行為。兩者相差一段時間差τ。從我們的研究中發現,τ約為1.1秒。我們將τ帶回原運動方程式,回推車輛的加速及減速過程。我們發現在不形成壅塞的前提下,密度最高只可達到每公尺0.67 輛車;而壅塞形成所需要的最低密度需為每公尺0.03輛車。此外,此壅塞移動的速率約為每秒1.36公尺。
We study the dynamics of the one-dimensional traffic flow through a car following model [1] which first proposed by Chandler et. al. We modify this model by introducing a distance factor and the repulsive Lennard-Jones potential to prevent car overtaking. The system that we are interested in is the one lane highway with the periodical boundary condition. The evolution of the jam which is caused by the unobvious perturbation was observed, and the fundamental diagram is shown.
The traffic flow would become unstable and forming the jam when the density goes beyond a threshold. The jam forming process can be divided into three stages: (1) piling and overshooting, (2) releasing, and (3) steady. From the observation of the numerical results, we propose the conjecture of repeating motion which states that after reaching the steady state, the vehicle would repeat the motion of that in front by a time shift τ. Our study reveals that τ was about 1.1 seconds. Substituting τ into the equation of motion, the accelerating and the decelerating curves of a vehicle are reconstructed. We conclude that the highest density which was reachable without the traffic jam is 0.66 cars per meter, and the minimum density required for the jam forming is 0.03 cars per meter. Furthermore, the propagating speed of the cluster is -1.36 m/s.
1 Introduction 1
2 Background 4
2.1 Chandler et. al. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Proportionate control . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Response lag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 Constant spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.4 Revisiting Proportionate Control . . . . . . . . . . . . . . . . . . . . 6
2.2 Bando et. al. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Cellular Automata Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Model and Algorithm 13
3.1 Our Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Numerical Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 System construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.2 Open boundary test . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.3 Method for measuring q and ρ . . . . . . . . . . . . . . . . . . . . . 16
4 Results and Discussion 18
4.1 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1.1 Simple perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1.2 With random velocity distribution in the beginning . . . . . . . . . . 19
4.1.3 Evolution of the collective properties . . . . . . . . . . . . . . . . . . 31
4.1.4 Fundamental diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.1 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.2 Deceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5 Conclusion 39
References 42
[1] B. S. Kerner, and H. Rehnorn, Phys. Rev. E 53, 4275 (1996).
[2] B. S. Kerner, and P. Konhäuser, Phys. Rev. E 50, 54 (1994).
[3] D. Helbing, Rev. Mod. Phys. 73, 1067 (2001).
[4] M. J. Lighthill, and G. B. Whitham, Proc. Royal Soc. 229, 317 (1955).
[5] R. E. Chandler, R. Herman, and E. W. Montroll, Oper. Res. 6, 165 (1958).
[6] M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Phys. Rev. E 51
1035 (1995).
[7] K. Nagel, and M. Schreckenberg, J. Phys. I France 2 2221 (1992).
[8] Yuki Sugiyama et. al., New J. Phys. 10 033001 (2008).
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