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Recently, the research on traffic flow system based on some classical models, such as cellular automata and car-following models, has attracted much attention. Some meaningful achievements have been obtained in the past few years by scholars from various fields. This paper starts with literature review on traffic flow theory studies. Car-following models, including the initial model proposed by Newell in 1961 (Newell G F 1961 Oper. Res. 9 209) and some later modified ones (e.g. full velocity difference model, or FVD model for short) have been deeply investigated. Based on Newell's car-following model, an extension of car-following model with consideration of vehicle-to-vehicle (V2V) communication is then developed. The vehicle-to-vehicle communication technology, which was proposed in the early 2000s, enable vehicles to collect traffic condition information from other vehicles (e.g. speed, headway, position, acceleration, etc.) and provide them for drivers in almost real time. Compared with those without V2V devices, drivers with information from V2V devices can react to traffic flow fluctuation timelier and more precisely. To represent the pre-reaction of drivers to traffic flow information provided by V2V devices, a parameter, , is newly introduced into Newell's car-following model. Then by second-order Taylor series expansion, a new car-following model with the influence of V2V (called V2V model) is proposed. Neutral stability condition of V2V model as well as phase diagram is derived theoretically with linear analysis method. The phase diagram of linear stability condition is divided into stable and unstable regions. By analyzing stability performance of the proposed model, it is evident that V2V communication technology can improve the stability of traffic flow system. Numerical simulation is demonstrated to study the influence of V2V devices on traffic flow on the one hand, and to acquire density waves as well as hysteresis loops under different values of parameter on the other hand. The sensitive analysis method are adopted as well.The numerical simulation results indicate that: 1) when compared with FVD model, V2V model can make vehicles react to traffic flow fluctuation earlier and reduce the speed changes under start-up, brake and incident conditions; this indicates that the consideration of V2V devices can improve the safety and ride comfort of traffic flow system; 2) the V2V model is sensitive to the value changes of parameter and T; the stability of traffic flow can be improved if the value of parameter increases, or parameter T decreases; this outcome precisely agrees with the above theoretical analysis; 3) the characteristics of traffic flow can influence the performance of V2V technology: compared with under low density condition, V2V communication technology can significantly increase the average speed of traffic flow under high density condition.
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Keywords:
- car-following model /
- vehicle-to-vehicle technology /
- linear analysis /
- numerical simulation
[1] Hua X D, Wang W, Wang H 2011 Acta Phys. Sin. 60 084502 (in Chinese) [华雪东, 王炜, 王昊 2011 物理学报 60 084502]
[2] Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199
[3] Helbing D 2001 Rev. Mod. Phys. 73 1067
[4] Tang T Q, Shi W F, Shang H Y, Wang Y P 2014 Nonlinear Dyn. 76 2017
[5] Lighthill M J, Whitham G B 1955 Proc. Roy. Soc. Ser. A 22 317
[6] Richards P I 1956 Oper. Res. 4 42
[7] Pipes L A 1969 Transpn. Res. 3 229
[8] Payne H J 1971 Models of Freeway Traffic and Control: Mathematical Models of Public Systems 1 51
[9] Kuhne R D 1984 Proceeding 9th International Symposium on Transportation and Traffic Theory Delft, Netherlands, July 11-13, 1984 p21
[10] Jiang R, Wu Q S, Zhu Z J 2002 Transp. Res. B 36 405
[11] Xue Y, Dai S Q 2003 Phys. Rev. E 68 066123
[12] Tang T Q, Caccetta L, Wu Y H, Huang H J, Yang X B 2014 J. Adv. Transp. 48 304
[13] Tang T Q, Shi W F, Yang X B, Wang Y P, Lu G Q 2013 Physica A 392 6300
[14] Peng G H, Song W, Peng Y J, Wang S H 2014 Physica A 398 76
[15] Redhu P, Gupta A K 2015 Physica A 421 249
[16] Gupta A K, Sharma S 2010 Chin. Phys. B 19 110503
[17] Gupta A K, Sharma S 2012 Chin. Phys. B 21 015201
[18] Peng G H, Cai X H, Cao B F, Liu C Q 2012 Physica A 391 656
[19] He Z C, Sun W B 2013 Acta Phys. Sin. 62 108901 (in Chinese) [何兆成, 孙文博 2013 物理学报 62 108901]
[20] Tang T Q, He J, Yang S C, Shang H Y 2014 Physica A 413 583
[21] Yu L, Shi Z K, Li T 2014 Phys. Lett. A 378 348
[22] Ge H X, Meng X P, Zhu H B, Li Z P 2014 Physica A 408 28
[23] Koutsopoulos H N, Farah H 2012 Transp. Res. B 46 563
[24] Ge H X, Yu J, Lo S M 2012 Chin. Phys. Lett. 29 50502
[25] Ge H X 2011 Chin. Phys. B 20 090502
[26] Zhou T, Sun L H, Zhao M, Li H M 2013 Chin. Phys. B 22 090205
[27] Punzo V, Ciuffo B, Montanino M 2012 Transp. Res. Rec. 2315 11
[28] Lakouari N, Bentaleb K, Ez-Zahraouy H, Benyoussef A 2015 Physica A 439 132
[29] Yang D, Qiu X P, Yu D, Sun R X, Pu Y 2015 Physica A 424 62
[30] Jing M, Deng W, Wang H, Ji Y J 2012 Acta Phys. Sin. 61 244502 (in Chinese) [敬明, 邓卫, 王昊, 季彦婕 2012 物理学报 61 244502]
[31] Feng S M, Li J Y, Ding N, Nie C 2015 Physica A 428 90
[32] Lrraga M E, Alvarez-Icaza L 2014 Chin. Phys. B 23 050701
[33] Qian Y S, Shi P J, Zeng Q, Ma C X, Lin F, Sun P, Wang H L 2010 Chin. Phys. B 19 048201
[34] Ez-Zahraouyt H, Jetto K, Benyoussef A 2006 Chin. J. Phys. 44 486
[35] Gazis D C, Herman R, Potts R B 1959 Oper. Res. 7 499
[36] Newell G F 1961 Oper. Res. 9 209
[37] Herman R, Montroll E W, Potts R B, Rothery R W 1959 Oper. Res. 7 86
[38] Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y 1995 Phys. Rev. E 51 1035
[39] Jiang R, Wu Q S, Zhu Z J 2001 Phys. Rev. 64 017101
[40] Knorr F, Schreckenberg M 2012 Physica A 391 2225
[41] Jin W L, Recker W W 2006 Transp. Res. B 40 230
[42] Kerner B S, Klenov S L, Brakemeier A 2008 Intelligent Vehicles Symposium (IEEE) Eindhoven, Netherlands, June 4-6, 2008 p180
[43] Ngoduy D, Hoogendoorn S P, Liu R 2009 Physica A 388 2705
[44] Helbing D, Tilch B 1998 Phys. Rev. E 58 133
[45] Zhou J 2015 Nonlinear Dyn. 81 549
[46] Zhao X, Gao Z Y 2005 Eur. Phys. J. B 47 145
[47] Zhao X, Gao Z Y 2007 Physica A 375 679
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[1] Hua X D, Wang W, Wang H 2011 Acta Phys. Sin. 60 084502 (in Chinese) [华雪东, 王炜, 王昊 2011 物理学报 60 084502]
[2] Chowdhury D, Santen L, Schadschneider A 2000 Phys. Rep. 329 199
[3] Helbing D 2001 Rev. Mod. Phys. 73 1067
[4] Tang T Q, Shi W F, Shang H Y, Wang Y P 2014 Nonlinear Dyn. 76 2017
[5] Lighthill M J, Whitham G B 1955 Proc. Roy. Soc. Ser. A 22 317
[6] Richards P I 1956 Oper. Res. 4 42
[7] Pipes L A 1969 Transpn. Res. 3 229
[8] Payne H J 1971 Models of Freeway Traffic and Control: Mathematical Models of Public Systems 1 51
[9] Kuhne R D 1984 Proceeding 9th International Symposium on Transportation and Traffic Theory Delft, Netherlands, July 11-13, 1984 p21
[10] Jiang R, Wu Q S, Zhu Z J 2002 Transp. Res. B 36 405
[11] Xue Y, Dai S Q 2003 Phys. Rev. E 68 066123
[12] Tang T Q, Caccetta L, Wu Y H, Huang H J, Yang X B 2014 J. Adv. Transp. 48 304
[13] Tang T Q, Shi W F, Yang X B, Wang Y P, Lu G Q 2013 Physica A 392 6300
[14] Peng G H, Song W, Peng Y J, Wang S H 2014 Physica A 398 76
[15] Redhu P, Gupta A K 2015 Physica A 421 249
[16] Gupta A K, Sharma S 2010 Chin. Phys. B 19 110503
[17] Gupta A K, Sharma S 2012 Chin. Phys. B 21 015201
[18] Peng G H, Cai X H, Cao B F, Liu C Q 2012 Physica A 391 656
[19] He Z C, Sun W B 2013 Acta Phys. Sin. 62 108901 (in Chinese) [何兆成, 孙文博 2013 物理学报 62 108901]
[20] Tang T Q, He J, Yang S C, Shang H Y 2014 Physica A 413 583
[21] Yu L, Shi Z K, Li T 2014 Phys. Lett. A 378 348
[22] Ge H X, Meng X P, Zhu H B, Li Z P 2014 Physica A 408 28
[23] Koutsopoulos H N, Farah H 2012 Transp. Res. B 46 563
[24] Ge H X, Yu J, Lo S M 2012 Chin. Phys. Lett. 29 50502
[25] Ge H X 2011 Chin. Phys. B 20 090502
[26] Zhou T, Sun L H, Zhao M, Li H M 2013 Chin. Phys. B 22 090205
[27] Punzo V, Ciuffo B, Montanino M 2012 Transp. Res. Rec. 2315 11
[28] Lakouari N, Bentaleb K, Ez-Zahraouy H, Benyoussef A 2015 Physica A 439 132
[29] Yang D, Qiu X P, Yu D, Sun R X, Pu Y 2015 Physica A 424 62
[30] Jing M, Deng W, Wang H, Ji Y J 2012 Acta Phys. Sin. 61 244502 (in Chinese) [敬明, 邓卫, 王昊, 季彦婕 2012 物理学报 61 244502]
[31] Feng S M, Li J Y, Ding N, Nie C 2015 Physica A 428 90
[32] Lrraga M E, Alvarez-Icaza L 2014 Chin. Phys. B 23 050701
[33] Qian Y S, Shi P J, Zeng Q, Ma C X, Lin F, Sun P, Wang H L 2010 Chin. Phys. B 19 048201
[34] Ez-Zahraouyt H, Jetto K, Benyoussef A 2006 Chin. J. Phys. 44 486
[35] Gazis D C, Herman R, Potts R B 1959 Oper. Res. 7 499
[36] Newell G F 1961 Oper. Res. 9 209
[37] Herman R, Montroll E W, Potts R B, Rothery R W 1959 Oper. Res. 7 86
[38] Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y 1995 Phys. Rev. E 51 1035
[39] Jiang R, Wu Q S, Zhu Z J 2001 Phys. Rev. 64 017101
[40] Knorr F, Schreckenberg M 2012 Physica A 391 2225
[41] Jin W L, Recker W W 2006 Transp. Res. B 40 230
[42] Kerner B S, Klenov S L, Brakemeier A 2008 Intelligent Vehicles Symposium (IEEE) Eindhoven, Netherlands, June 4-6, 2008 p180
[43] Ngoduy D, Hoogendoorn S P, Liu R 2009 Physica A 388 2705
[44] Helbing D, Tilch B 1998 Phys. Rev. E 58 133
[45] Zhou J 2015 Nonlinear Dyn. 81 549
[46] Zhao X, Gao Z Y 2005 Eur. Phys. J. B 47 145
[47] Zhao X, Gao Z Y 2007 Physica A 375 679
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