Flow difference effect in the lattice hydrodynamic model

doi:10.1088/1674-1056/19/4/040303

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40303-040303.doi: 10.1088/1674-1056/19/4/040303

Flow difference effect in the lattice hydrodynamic model

田钧方, 贾斌, 李新刚, 高自友

MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China

收稿日期:2009-08-10 修回日期:2009-09-27 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
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.~

Flow difference effect in the lattice hydrodynamic model

Tian Jun-Fang(田钧方), Jia Bin(贾斌)^†, Li Xing-Gang(李新刚), and Gao Zi-You(高自友)

MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China

Received:2009-08-10 Revised:2009-09-27 Online:2010-04-15 Published:2010-04-15
Supported by:
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.~

摘要/Abstract

摘要： 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.

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.

Key words: lattice hydrodynamic model, traffic flow, flow difference

中图分类号: (Solitary waves)

47.35.Fg

47.11.-j (Computational methods in fluid dynamics) 45.70.Vn (Granular models of complex systems; traffic flow)

田钧方, 贾斌, 李新刚, 高自友. Flow difference effect in the lattice hydrodynamic model[J]. 中国物理B, 2010, 19(4): 40303-040303.

Tian Jun-Fang(田钧方), Jia Bin(贾斌), Li Xing-Gang(李新刚), and Gao Zi-You(高自友). Flow difference effect in the lattice hydrodynamic model[J]. Chin. Phys. B, 2010, 19(4): 40303-040303.

参考文献 32

[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

Flow difference effect in the lattice hydrodynamic model

Flow difference effect in the lattice hydrodynamic model

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