Nonlinear analysis of traffic jams in an anisotropic continuum model

doi:10.1088/1674-1056/19/11/110503

中国物理B ›› 2010, Vol. 19 ›› Issue (11): 110503-110507.doi: 10.1088/1674-1056/19/11/110503

Nonlinear analysis of traffic jams in an anisotropic continuum model

Arvind Kumar Gupta¹, Sapna Sharma²

(1)Department of Mathematics, IIT Ropar-140001, India; (2)Mathematics Group, Birla Institute of Technology and Science, Pilani-333031, India

收稿日期:2009-11-04 修回日期:2010-05-18 出版日期:2010-11-15 发布日期:2010-11-15

Nonlinear analysis of traffic jams in an anisotropic continuum model

Arvind Kumar Gupta^a)† and Sapna Sharma^b)

^a Department of Mathematics, IIT Ropar-140001, India; ^b Mathematics Group, Birla Institute of Technology and Science, Pilani-333031, India

Received:2009-11-04 Revised:2010-05-18 Online:2010-11-15 Published:2010-11-15

摘要/Abstract

摘要： This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. In order to establish traffic flow stability criterion or to know the critical parameters that lead, on one hand, to a stable response to perturbations or disturbances or, on the other hand, to an unstable response and therefore to a possible congestion, a nonlinear stability criterion is derived by using a wavefront expansion technique. The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter. It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods. Moreover, the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.

Abstract: This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. In order to establish traffic flow stability criterion or to know the critical parameters that lead, on one hand, to a stable response to perturbations or disturbances or, on the other hand, to an unstable response and therefore to a possible congestion, a nonlinear stability criterion is derived by using a wavefront expansion technique. The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter. It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods. Moreover, the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.

Key words: traffic flow, non-linear stability, wavefront method

中图分类号: (Functional analysis)

02.30.Sa

89.40.Bb (Land transportation)

Arvind Kumar Gupta, Sapna Sharma. Nonlinear analysis of traffic jams in an anisotropic continuum model[J]. 中国物理B, 2010, 19(11): 110503-110507.

Arvind Kumar Gupta and Sapna Sharma. Nonlinear analysis of traffic jams in an anisotropic continuum model[J]. Chin. Phys. B, 2010, 19(11): 110503-110507.

参考文献 35

[1]	Gerlough D L and Huber M J 1975 em Special Report No 165 (Washington, DC: Transportation Research Board, National Research Council)
[2]	Helbing D 2001 Rev. Mod. Phys. 73 1067
[3]	Wong G C K and Wong S C 2002 Trans. Res. A 36 827
[4]	Lighthill M J and Whitham G B 1955 Proc. R. Soc. London Ser. A 229 317
[5]	Richards P I 1956 Operations Research 4 42
[6]	Zhang H M 2003 Trans. Res. B 37 101
[7]	Lax P D 1972 Society for Industrial and Applied Mathematics (Philadelphia, PA)
[8]	Payne H J 1971 Mathematical Models of Public Systems In: Bekey G A (Ed.) Simulation Councils Proceedings Series 1 51
[9]	Phillips W F 1979 Trans. Plann. Technol. 5 131
[10]	Kerner B S and Konh"auser P 1993 Phys. Rev. E 48 2335
[11]	Zhang H M 1998 Trans. Res. B 32 (7) 485
[12]	Berg P, Mason A and Woods A 2000 Phys. Rev. E 61 1056
[13]	Bando M, Hasebe K, Nakayama A, Shibata A and Sugiyama Y 1995 Phys. Rev. E 51 1035
[14]	Daganzo C F 1995 Trans. Res. B 29 277
[15]	Zhang H M 2000 Trans. Res. B 34 583
[16]	Treiber M, Hennecke A and Helbing D 1999 Phys. Rev. E 59 239
[17]	Zhang H M 2002 Trans. Res. B 36 275
[18]	Zhang H M 2003 Trans. Res. B 37 27
[19]	Gupta A K and Katiyar V K 2005 J. Phys. A 38 4069
[20]	Gupta A K and Katiyar V K 2006 Physica A 368 551
[21]	Jiang R, Wu Q and Zhu Z 2002 Trans. Res. B 36 405
[22]	Holland E N 1998 Trans. Res. B 32 141
[23]	Whitham G B 1974 Linear and Nonlinear Waves (New York: John Wiley & Sons Inc)
[24]	Swaroop D and Rajagopal K R 1999 Trans. Res. C 7 329
[25]	Zhang H M 1999 Trans. Res. B 33 399
[26]	Del Castillo J M 2001 Trans. Res. B 35 367
[27]	Yi J G, Lin H, Alvarez L and Horowitz R 2003 Trans. Res. B 37 661
[28]	Ou Z H, Dai S Q, Zhang P and Dong L Y 2007 SIAM J. Appl. Math. 67 605
[29]	Ou Z H 2005 Physica A 351 620
[30]	Ou Z H, Dai S Q, Dong L Y, Wu Z and Tao M D 2006 Physica A 362 525
[31]	Helbing D and Johansson A F 2009 Eur. Phys. J. B 69 549
[32]	Zhang H M 2009 Eur. Phys. J. B 69 563
[33]	Helbing D 2002 Math. Comput. Modelling 35 517
[34]	Kerner B S and Konh"auser P 1994 Phys. Rev. E 50 (1) 54
[35]	Herrmann M and Kerner B S 1998 Physica A 255 163 endfootnotesize

Nonlinear analysis of traffic jams in an anisotropic continuum model

Nonlinear analysis of traffic jams in an anisotropic continuum model

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 35

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity[J]. 中国物理B, 2023, 32(3): 30203-030203.
[2]	Wenjie Yang(杨文杰). Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation[J]. 中国物理B, 2022, 31(2): 20201-020201.
[3]	M. Syed Ali. Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays[J]. 中国物理B, 2014, 23(6): 60702-060702.
[4]	姚静荪, 林万涛, 杜增吉, 莫嘉琪. Asymptotic solving method for period solution to a class of disturbed nonlinear evolution equation[J]. Chin. Phys. B, 2012, 21(12): 120205-120205.
[5]	M. Syed Ali. Novel delay dependent stability analysis of Takagi–Sugeno fuzzy uncertain neural networks with time varying delays[J]. 中国物理B, 2012, 21(7): 70207-070207.
[6]	汪娜. Existence of periodic solutions for the nonlinear functional differential equation in the lossless transmission line model[J]. 中国物理B, 2012, 21(1): 10202-010202.
[7]	M. Syed Ali. Robust stability analysis of Takagi–Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays[J]. 中国物理B, 2011, 20(8): 80201-080201.
[8]	张荣, 徐振源. Function projective synchronization in partially linear drive–response chaotic systems[J]. 中国物理B, 2010, 19(12): 120511-120511.
[9]	贾利群, 解银丽, 张耀宇, 杨新芳. A type of new conserved quantity deduced from Mei symmetry for Appell equations in a holonomic system with unilateral constraints[J]. 中国物理B, 2010, 19(11): 110301-110306.
[10]	范洪义, 任刚, 胡利云, 姜年权. Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation[J]. 中国物理B, 2010, 19(11): 114206-114208.
[11]	莫嘉琪, 陈贤峰. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. 中国物理B, 2010, 19(10): 100203-100203.
[12]	李军民, 梁祖峰, 唐晓艳. Interaction behaviours of solitoffs: fission, fusion, reconnection and annihilation[J]. 中国物理B, 2010, 19(10): 100205-100205.
[13]	潘震环, 马松华, 方建平. Instantaneous solitons and fractal solitons for a (2+1)-dimensional nonlinear system[J]. 中国物理B, 2010, 19(10): 100301-100301.
[14]	赵国忠, 蔚喜军, 徐云, 朱江, 吴迪. Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation[J]. 中国物理B, 2010, 19(8): 80204-080204.
[15]	套格图桑, 斯仁道尔吉, 李姝敏. New application to Riccati equation[J]. 中国物理B, 2010, 19(8): 80303-080303.