宏观交通流模型的能耗研究

梁家源; 滕维中; 薛郁

doi:10.7498/aps.62.024706

摘要

本文在几种典型的宏观交通流模型的基础上, 导出能量耗散的计算公式, 宏观交通流模型能耗不同于元胞自动机交通模型, 其能耗不仅考虑车流速度减少, 而且还要计及通过路段的车流通量引起的能耗. 通过对满足黎曼初始条件的道路能耗和道路交通瓶颈处能耗的计算和理论分析, 表明交通拥堵处, 能量耗散比较高, 而且能量耗散的变化也能反映交通拥堵产生及消散的情况.

关键词:

In this paper, the energy dissipation formulas of the several typical macroscopic continuum models of traffic flow are derived according to the loss of the kinetic energy of traffic flow on road. The calculation of energy dissipation via two traffic cases: two Riemann initial conditions and the traffic bottleneck on the road indicates the energy dissipation of macroscopic traffic mode is influenced by not only the velocity reduction of the vehicle, but also the velocity gradient of the vehicle and the traffic density along the road, which is different from the result obtained from the CA model.

Keywords:

作者及机构信息

1.
广西大学物理科学与工程技术学院, 南宁 530004

基金项目: 国家自然科学基金(批准号: 11262003和11047003)、广西壮族自治区"十百千人才工程"专项基金(批准号: 2005205)、香港城市大学战略研究基金(批准号: 7002718 (CA))和广西壮族自治区研究生创新项目(批准号: 105930903077)资助的课题.

Authors and contacts

1.
Institute of Physical Science and Engineering, Guangxi University, Nanning 53004, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11262003 and 11047003) , the Special Foundation for the New Century Talents Program of Guangxi Zhuang Autonomous Region (Grant No. 2005205), CityU Strategic Research Grant (SRG) of HK( PROJECT NO.: 7002718 (CA)), and the Graduate Student Innovative Foundation of Guangxi Zhuang Autonomous Region (No. 105930903077).

参考文献

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[10]	Maerivoet S, De Moor B 2005 Phys. Rep. 419 1
[11]	Nagel K, Schreckenberg M 1992 J. Phys. I 2 2221
[12]	Helbing D 1997 Phys. Rev. E 55 3735
[13]	Lighthill M J, Whitham G B 1955 Proc. Roy. Soc. Ser. A 22 317
[14]	Richards P I 1956 Oper. Res. 4 42
[15]	Pipes L A 1969 Transpn. Res. 3 229
[16]	Payne H J 1971 Math. Meth. of Pub. Sys. 1 p51
[17]	Khne R D 1984 Proc 9th Int on Trans and Traff. Theor. Delft, Netherlands, July 11-13, 1984 p21
[18]	Feng S W 1998 Ph. D. Dissertation (Shanghai: Shanghai University) (in Chinese) [冯苏苇 1998 博士学位论文 (上海:上海大学)]
[19]	Zhang H M 1998 Transp. Res. B 32 485
[20]	Jiang R, Wu Q S, Zhu Z J 2002 Transp. Res. B 36 405
[21]	Xue Y, Dai S Q 2003 Phys. Rev. E 68 066123
[22]	Ou Yang M G 2006 Sci. & Tech. Industry of China 2 8 (in Chinese) [欧阳明高 2006 中国科技产业 2 8]
[23]	Nakayama Y, Sugiyama Y, Hasebe K 2002 Phys. Rev. E 65 016112
[24]	Shi W, Xue Y 2007 Physica A 381 399
[25]	Zhang W, Yang X Q 2008 Physica A 387 4657
[26]	Tian H H, Xue Y, Kang S J, Liang Y J. 2009 Acta Phys. Sin. 58 4506 (in Chinese) [田欢欢, 薛郁, 康三军, 梁玉娟 2009 58 4506]
[27]	Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 55 634]
[28]	Landau L D, Lifshitz E M 1987 Fluid Mechanics (2th Ed.) (Oxford: Pergamon Press) p50
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施引文献

[1]	Helbing D, Hennecke A, Treiber M 1999 Phy. Rev. Lett. 82 4360
[2]	Helbing D, Hennecke A, Shvetsov V, Treiber M 2001 Transpn. Res. B 35 180
[3]	Kerner B S, Konhäuser P 1997 Phy. Rev. Lett. 49 4030
[4]	Kerner B S, Rehborn H 1996 Phy. Rev. E 53 R4275
[5]	Chowdhury D, Santen L, Schreckenberg A 2000 Phys. Rept. 329 199
[6]	Biham O, Middleton A, Levine D 1992 Phys. Rev. A 46 R6124
[7]	Fukui M, Ishibashi Y 1996 J. Phys. Soc. Jpn. 65 1868
[8]	Wang B H, Kuang Y Q, Xu B M 1998 Acta Phys. Sin. 47 906 (in Chinese) [汪秉宏, 邝乐琪, 许伯铭 1998 47 906]
[9]	Xue Y, Dong L Y, Dai S Q 2001 Acta Phys. Sin. 50 445 (in Chinese) [薛郁, 董力耘 2001 50 445]
[10]	Maerivoet S, De Moor B 2005 Phys. Rep. 419 1
[11]	Nagel K, Schreckenberg M 1992 J. Phys. I 2 2221
[12]	Helbing D 1997 Phys. Rev. E 55 3735
[13]	Lighthill M J, Whitham G B 1955 Proc. Roy. Soc. Ser. A 22 317
[14]	Richards P I 1956 Oper. Res. 4 42
[15]	Pipes L A 1969 Transpn. Res. 3 229
[16]	Payne H J 1971 Math. Meth. of Pub. Sys. 1 p51
[17]	Khne R D 1984 Proc 9th Int on Trans and Traff. Theor. Delft, Netherlands, July 11-13, 1984 p21
[18]	Feng S W 1998 Ph. D. Dissertation (Shanghai: Shanghai University) (in Chinese) [冯苏苇 1998 博士学位论文 (上海:上海大学)]
[19]	Zhang H M 1998 Transp. Res. B 32 485
[20]	Jiang R, Wu Q S, Zhu Z J 2002 Transp. Res. B 36 405
[21]	Xue Y, Dai S Q 2003 Phys. Rev. E 68 066123
[22]	Ou Yang M G 2006 Sci. & Tech. Industry of China 2 8 (in Chinese) [欧阳明高 2006 中国科技产业 2 8]
[23]	Nakayama Y, Sugiyama Y, Hasebe K 2002 Phys. Rev. E 65 016112
[24]	Shi W, Xue Y 2007 Physica A 381 399
[25]	Zhang W, Yang X Q 2008 Physica A 387 4657
[26]	Tian H H, Xue Y, Kang S J, Liang Y J. 2009 Acta Phys. Sin. 58 4506 (in Chinese) [田欢欢, 薛郁, 康三军, 梁玉娟 2009 58 4506]
[27]	Wang T, Gao Z Y, Zhao X M 2006 Acta Phys. Sin. 55 634 (in Chinese) [王涛, 高自友, 赵小梅 2006 55 634]
[28]	Landau L D, Lifshitz E M 1987 Fluid Mechanics (2th Ed.) (Oxford: Pergamon Press) p50
[29]	Del Castillo J M, Bentez F G 1995 Transp. Res. B 29 373
[30]	Babcock P S, Auslander D M, Tomizuka M, May A D 1984 Transpn. Res. Rec. 971 80

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