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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.
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Keywords:
- energy dissipation /
- traffic flow /
- macroscopic traffic model /
- fluid mechanics
[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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[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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