Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(4): 040303    DOI: 10.1088/1674-1056/19/4/040303
GENERAL Prev   Next  

Flow difference effect in the lattice hydrodynamic model

Tian Jun-Fang, Jia Bin, Li Xing-Gang, Gao Zi-You
MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China
Abstract  In this paper, a new lattice hydrodynamic model based on Nagatani's model [Nagatani T 1998 Physica A 261 599] is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink--antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.
Keywords:  lattice hydrodynamic model      traffic flow      flow difference  
Received:  10 August 2009      Revised:  27 September 2009      Accepted manuscript online: 
PACS:  47.35.Fg (Solitary waves)  
  47.11.-j (Computational methods in fluid dynamics)  
  45.70.Vn (Granular models of complex systems; traffic flow)  
Fund: Project supported by the National Basic Research Program of China (Grant No.~G2006CB705500), the National Natural Science Foundation of China (Grant Nos.~70501004, 70701004 and 70631001), Program for New Century Excellent Talents in University (Grant No.~

Cite this article: 

Tian Jun-Fang, Jia Bin, Li Xing-Gang, Gao Zi-You Flow difference effect in the lattice hydrodynamic model 2010 Chin. Phys. B 19 040303

[1] Chowdhury D, Santen L and Schadschneider A 2000 Phys. Rep.] 329 199
[2] Helbing D 2001 Rev. Mod. Phys. 73 1067
[3] Kerner B S 2004 The Physics of Traffic (Heidelberg: Springer)
[4] Nagatani T 2002 Rep. Prog. Phys. 65 1331
[5] Helbing D 2000 Traffic and Granular Flow 99 (Heidelberg: Springer)
[6] Jia B, Gao Z Y, Li K P and Li X G 2007 Models and Simulations of Traffic System Based on the Theory of Cellular Automaton (Beijing: Science Press)
[7] Herman R, Montrol E W, Potts R B and Rothery R W 1959 Oper. Res. 7 86
[8] Newell G F 1961 Oper. Res. 9 209
[9] Bando M, Hasebe K, Nakayama A, Shibata A and Sugiyama Y 1995 Phys. Rev. E 51 1035
[10] Treiber M, Hennecke A and Helbing D 2000 Phys. Rev. E 62 1805
[11] Nagel K and Schreckenberg M 1992 J. Phys. A 2 2221
[12] Li X B, Wu Q S and Jiang R 2001 Phys. Rev. E 64 066128
[13] Jiang R and Wu Q S 2003 J. Phys. A: Math. Gen. 36] 381
[14] Kerner B S, Klenov L S and Wolf D E 2002 J. Phys. A: Math. Gen. 35 9971
[15] Prigogine I and Herman R 1971 Kinetic of Vehicular Traffic (New York: Elsevier)
[16] Helbing D 1996 Phys. Rev. E 53 2366
[17] Kerner B S and Konhauser P 1993 Phys. Rev. E 48 2335
[18] Ge H X, Zhu H B and Dai S Q 2005 Acta Phys. Sin. 54 4621 (in Chinese)
[19] Wang T, Gao Z Y and Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese)
[20] Li K P, Gao Z Y and Mao B H 2007 Chin. Phys. 16 359
[21] Xue Y 2002 Chin. Phys. 11 1128
[22] Nagatani T 1998 Physica A 261 599
[23] Nagatani T 1999 Physica A 264 581
[24] Xue Y 2004 Acta Phys. Sin. 53 25 (in Chinese)
[25] Ge H X, Dai S Q, Xue Y and Dong L Y 2005 Phys. Rev. E 71] 066119
[26] Nagatani T and Cheng R J 2008 Physica A 387 6952
[27] Nagatani T 1999 Physica A 265 297
[28] Nagatani T 1999 Physica A 272 592
[29] Jiang R, Wu Q S and Zhu Z J 2001 Phys. Rev. E 64 017101
[30] Kurtze D A and Hong D C 1995 Phys. Rev. E 52 218
[31] Komatsu T and Sasa S 1995 Phys. Rev. E 52 5574
[32] Ge H X, Cheng R J and Dai S Q 2005 Physica A 357 466
[1] Modeling and analysis of car-following behavior considering backward-looking effect
Dongfang Ma(马东方), Yueyi Han(韩月一), Fengzhong Qu(瞿逢重), and Sheng Jin(金盛). Chin. Phys. B, 2021, 30(3): 034501.
[2] A new car-following model with driver's anticipation effect of traffic interruption probability
Guang-Han Peng(彭光含). Chin. Phys. B, 2020, 29(8): 084501.
[3] A macroscopic traffic model based on weather conditions
Zawar H. Khan, Syed Abid Ali Shah, T. Aaron Gulliver. Chin. Phys. B, 2018, 27(7): 070202.
[4] A new control method based on the lattice hydrodynamic model considering the double flux difference
Shunda Qin(秦顺达), Hongxia Ge(葛红霞), Rongjun Cheng(程荣军). Chin. Phys. B, 2018, 27(5): 050503.
[5] Traffic flow velocity disturbance characteristics and control strategy at the bottleneck of expressway
Jun-Wei Zeng(曾俊伟), Yong-Sheng Qian(钱勇生), Xu-Ting Wei(魏谞婷), Xiao Feng(冯骁). Chin. Phys. B, 2018, 27(12): 124502.
[6] Stability analysis of traffic flow with extended CACC control models
Ya-Zhou Zheng(郑亚周), Rong-Jun Cheng(程荣军), Siu-Ming Lo(卢兆明), Hong-Xia Ge(葛红霞). Chin. Phys. B, 2016, 25(6): 060506.
[7] A new traffic model on compulsive lane-changing caused by off-ramp
Xiao-He Liu(刘小禾), Hung-Tang Ko(柯鸿堂), Ming-Min Guo(郭明旻), Zheng Wu(吴正). Chin. Phys. B, 2016, 25(4): 048901.
[8] A new cellular automata model of traffic flow with negative exponential weighted look-ahead potential
Xiao Ma(马骁), Wei-Fan Zheng(郑伟范), Bao-Shan Jiang(江宝山), Ji-Ye Zhang(张继业). Chin. Phys. B, 2016, 25(10): 108902.
[9] A new traffic model with a lane-changing viscosity term
Ko Hung-Tang, Liu Xiao-He, Guo Ming-Min, Wu Zheng. Chin. Phys. B, 2015, 24(9): 098901.
[10] A cellular automata model of traffic flow with variable probability of randomization
Zheng Wei-Fan, Zhang Ji-Ye. Chin. Phys. B, 2015, 24(5): 058902.
[11] A new coupled map car-following model considering drivers’ steady desired speed
Zhou Tong, Sun Di-Hua, Li Hua-Min, Liu Wei-Ning. Chin. Phys. B, 2014, 23(5): 050203.
[12] Biham-Middleton-Levine model in consideration of cooperative willingness
Pan Wei, Xue Yu, Zhao Rui, Lu Wei-Zhen. Chin. Phys. B, 2014, 23(5): 058902.
[13] Cellular automata model for traffic flow with safe driving conditions
María Elena Lárraga, Luis Alvarez-Icaza. Chin. Phys. B, 2014, 23(5): 050701.
[14] A control method applied to mixed traffic flow for the coupled-map car-following model
Cheng Rong-Jun, Han Xiang-Lin, Lo Siu-Ming, Ge Hong-Xia. Chin. Phys. B, 2014, 23(3): 030507.
[15] On the modeling of synchronized flow in cellular automaton models
Jin Cheng-Jie, Wang Wei, Jiang Rui. Chin. Phys. B, 2014, 23(2): 024501.
No Suggested Reading articles found!