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Stability analysis and fundamental diagram of heterogeneous traffic flow mixed with cooperative adaptive cruise control vehicles

Qin Yan-Yan Wang Hao Wang Wei Wan Qian

Stability analysis and fundamental diagram of heterogeneous traffic flow mixed with cooperative adaptive cruise control vehicles

Qin Yan-Yan, Wang Hao, Wang Wei, Wan Qian
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  • This paper is aimed at building a framework for string stability analysis of traffic flow mixed with different cooperative adaptive cruise control (CACC) market penetration rates. In addition to the string stability, the fundamental diagram of the mixed flow is also taken into consideration for evaluating the effect of CACC vehicles on capacity. In order to describe the car-following dynamics of real CACC vehicles, the CACC model proposed by PATH is employed, which is validated by real experimental data. The intelligent driver model (IDM) is used as a surrogate car-following model for traditional manual driven vehicles. Based on the guidelines proposed by Ward[Ward J A 2009 Ph. D. Dissertation (Bristol:University of Bristol)], a framework is developed for the analytical investigation of heterogeneous traffic flow string stability. The framework presented considers the instability condition of traffic flow as a linear function of CACC market penetration rate. Following the framework, the string stabilities of the mixed traffic flow under different CACC market penetration rates and equilibrium velocities are analyzed. For fundamental diagram of the heterogeneous traffic flow, the equilibrium velocity-spacing functions of manual vehicles and CACC vehicles are obtained respectively based on car-following model. Then, the fundamental diagram of the density-velocity relationship of the heterogeneous traffic flow is derived based on the definition of traffic flow density. In addition, the theoretical fundamental diagram is plotted to show the property of traffic throughput. The numerical simulations are also carried out in order to investigate the effect of CACC vehicle on the characteristics of fundamental diagram. Besides, sensitivity analyses on CACC desired time gap are conducted for both string stability and fundamental diagram. Analytical studies and simulation results are as follows. 1) The heterogeneous traffic flow is stable for different equilibrium velocities and CACC market penetration rates, if manual driven vehicles are stable. Otherwise, the instability of traditional traffic flow is improved gradually with the increase of the CACC market penetration rate. Additionally, the stability will become better when equilibrium velocity is away from the velocity range of 9.6-18.6 m/s. 2) Because CACC vehicles can travel at free-flow speed in a relatively small headway, CACC vehicles can improve the capacity of heterogeneous traffic flow. 3) The results of sensitivity analysis indicate that with the increase of the CACC desired time gap, the stable region of heterogeneous traffic flow increases. However, the capacity of the fundamental diagram drops. Therefore, the value of the desired time gap should be determined with considering the effects of the two aspects on the heterogeneous traffic flow. It is noted that the CACC model used in this paper is based on the current state-of-the-art real CACC vehicle experiments. In the future, more experimental observations will yield new CACC models. However, the framework presented in this paper can still be used for the analytical investigation of string stability of the heterogeneous traffic flow at that time.
      Corresponding author: Wang Hao, haowang@seu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51478113, 51508122), the Foundation for Excellent Young Scientists of Southeast University, China (Grant No. 2242015R30028), and the Guangxi Science and Technology Project, China (Grant No. 15248002-10).
    [1]

    Tang T Q, Yi Z Y, Lin Q F 2017 Physica A 469 200

    [2]

    Ranjitkar P, Nakatsuji T, Kawamura A 2005 Transp. Res. Rec. 1934 22

    [3]

    Jiang R, Hu M B, Zhang H M, Gao Z Y, Jia B, Wu Q S 2015 Transp. Res. Part B: Methodol. 80 338

    [4]

    Pueboobpaphan R, van Arem B 2010 Transp. Res. Rec. 2189 89

    [5]

    Kerner B S 2016 Physica A 450 700

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    Naus G J L, Vugts R P A, Ploeg J, Molengraft M J G, Steinbuch M 2010 IEEE Trans. Veh. Technol. 59 4268

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    Milans V, Shladover S E, Spring J, Nowakowski C, Kawazoe H, Nakamura M 2014 IEEE Trans. Intell. Transp. Syst. 15 296

    [8]

    Milans V, Villagr J, Prez J, Gonzlez C 2012 IEEE Trans. Ind. Electron. 59 620

    [9]

    Jin I G, Orosz G 2014 Transp. Res. C 46 46

    [10]

    Tang T Q, Chen L, Yang S C, Shang H Y 2015 Physica A 430 148

    [11]

    Ge H X, Cui Y, Zhu K Q, Cheng R J 2015 Commun. Nonlinear Sci. Numer. Simulat. 22 903

    [12]

    Ge H X, Zheng P J, Wang W, Cheng R J 2015 Physica A 433 274

    [13]

    Tang T Q, Li J G, Yang S C, Shang H Y 2015 Physica A 419 293

    [14]

    Sau J, Monteil J, Billot R, Faouzi N E E 2014 Transp. B: Transp. Dyn. 2 60

    [15]

    Wang M, Daamen W, Hoogendoorn S P, van Arem B 2016 IEEE Trans. Intell. Transp. Syst. 17 1459

    [16]

    van Arem B, van Driel C J G, Visser R 2006 IEEE Trans. Intell. Transp. Syst. 7 429

    [17]

    Tang T Q, Xu K W, Yang S C, Ding C 2016 Physica A 441 221

    [18]

    Jerath K, Brennan S N 2012 IEEE Trans. Intell. Transp. Syst. 13 1782

    [19]

    Tang T Q, Yu Q, Yang S C, Ding C 2015 Mod. Phys. Lett. B 29 1550157

    [20]

    Milans V, Shladover S E 2014 Transp. Res. C 48 285

    [21]

    Ge H X, Cheng R J, Li Z P 2008 Physica A 387 5239

    [22]

    Yu S, Shi Z 2015 Physica A 428 206

    [23]

    Hua X D, Wang W, Wang H 2016 Acta Phys. Sin. 65 010502 (in Chinese) [华雪东, 王炜, 王昊 2016 物理学报 65 010502]

    [24]

    Hua X D, Wang W, Wang H 2016 Acta Phys. Sin. 65 084503 (in Chinese) [华雪东, 王炜, 王昊 2016 物理学报 65 084503]

    [25]

    Ward J A 2009 Ph. D. Dissertation (Bristol: University of Bristol)

    [26]

    Treiber M, Hennecke A, Helbing D 2000 Phys. Rev. E 62 1805

    [27]

    Kesting A, Treiber M, Schnhof M, Helbing D 2008 Transp. Res. C 16 668

    [28]

    Shladover S, Su D, Lu X Y 2012 Transp. Res. Rec. 2324 63

    [29]

    Ma X, Zheng W F, Jiang B S, Zhang J Y 2016 Chin. Phys. B 25 108902

    [30]

    Wilson R E 2008 Phil. Trans. R. Soc. A 366 2017

    [31]

    Zheng Y Z, Cheng R J, Lu Z M, Ge H X 2016 Chin. Phys. B 25 060506

    [32]

    Zheng W F, Zhang J Y 2015 Chin. Phys. B 24 058902

    [33]

    Ge H X, Meng X P, Zhu K Q, Cheng R J 2014 Chin. Phys. Lett. 31 080505

    [34]

    Tang T Q, Li C Y, Huang H J 2010 Phys. Lett. A 374 3951

    [35]

    Liu Y J, Zhang H L, He L 2012 Chin. Phys. Lett. 29 104502

    [36]

    Oh S, Yeo H 2012 Transp. Res. Rec. 2286 111

  • [1]

    Tang T Q, Yi Z Y, Lin Q F 2017 Physica A 469 200

    [2]

    Ranjitkar P, Nakatsuji T, Kawamura A 2005 Transp. Res. Rec. 1934 22

    [3]

    Jiang R, Hu M B, Zhang H M, Gao Z Y, Jia B, Wu Q S 2015 Transp. Res. Part B: Methodol. 80 338

    [4]

    Pueboobpaphan R, van Arem B 2010 Transp. Res. Rec. 2189 89

    [5]

    Kerner B S 2016 Physica A 450 700

    [6]

    Naus G J L, Vugts R P A, Ploeg J, Molengraft M J G, Steinbuch M 2010 IEEE Trans. Veh. Technol. 59 4268

    [7]

    Milans V, Shladover S E, Spring J, Nowakowski C, Kawazoe H, Nakamura M 2014 IEEE Trans. Intell. Transp. Syst. 15 296

    [8]

    Milans V, Villagr J, Prez J, Gonzlez C 2012 IEEE Trans. Ind. Electron. 59 620

    [9]

    Jin I G, Orosz G 2014 Transp. Res. C 46 46

    [10]

    Tang T Q, Chen L, Yang S C, Shang H Y 2015 Physica A 430 148

    [11]

    Ge H X, Cui Y, Zhu K Q, Cheng R J 2015 Commun. Nonlinear Sci. Numer. Simulat. 22 903

    [12]

    Ge H X, Zheng P J, Wang W, Cheng R J 2015 Physica A 433 274

    [13]

    Tang T Q, Li J G, Yang S C, Shang H Y 2015 Physica A 419 293

    [14]

    Sau J, Monteil J, Billot R, Faouzi N E E 2014 Transp. B: Transp. Dyn. 2 60

    [15]

    Wang M, Daamen W, Hoogendoorn S P, van Arem B 2016 IEEE Trans. Intell. Transp. Syst. 17 1459

    [16]

    van Arem B, van Driel C J G, Visser R 2006 IEEE Trans. Intell. Transp. Syst. 7 429

    [17]

    Tang T Q, Xu K W, Yang S C, Ding C 2016 Physica A 441 221

    [18]

    Jerath K, Brennan S N 2012 IEEE Trans. Intell. Transp. Syst. 13 1782

    [19]

    Tang T Q, Yu Q, Yang S C, Ding C 2015 Mod. Phys. Lett. B 29 1550157

    [20]

    Milans V, Shladover S E 2014 Transp. Res. C 48 285

    [21]

    Ge H X, Cheng R J, Li Z P 2008 Physica A 387 5239

    [22]

    Yu S, Shi Z 2015 Physica A 428 206

    [23]

    Hua X D, Wang W, Wang H 2016 Acta Phys. Sin. 65 010502 (in Chinese) [华雪东, 王炜, 王昊 2016 物理学报 65 010502]

    [24]

    Hua X D, Wang W, Wang H 2016 Acta Phys. Sin. 65 084503 (in Chinese) [华雪东, 王炜, 王昊 2016 物理学报 65 084503]

    [25]

    Ward J A 2009 Ph. D. Dissertation (Bristol: University of Bristol)

    [26]

    Treiber M, Hennecke A, Helbing D 2000 Phys. Rev. E 62 1805

    [27]

    Kesting A, Treiber M, Schnhof M, Helbing D 2008 Transp. Res. C 16 668

    [28]

    Shladover S, Su D, Lu X Y 2012 Transp. Res. Rec. 2324 63

    [29]

    Ma X, Zheng W F, Jiang B S, Zhang J Y 2016 Chin. Phys. B 25 108902

    [30]

    Wilson R E 2008 Phil. Trans. R. Soc. A 366 2017

    [31]

    Zheng Y Z, Cheng R J, Lu Z M, Ge H X 2016 Chin. Phys. B 25 060506

    [32]

    Zheng W F, Zhang J Y 2015 Chin. Phys. B 24 058902

    [33]

    Ge H X, Meng X P, Zhu K Q, Cheng R J 2014 Chin. Phys. Lett. 31 080505

    [34]

    Tang T Q, Li C Y, Huang H J 2010 Phys. Lett. A 374 3951

    [35]

    Liu Y J, Zhang H L, He L 2012 Chin. Phys. Lett. 29 104502

    [36]

    Oh S, Yeo H 2012 Transp. Res. Rec. 2286 111

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    [2] Jia Ning, Ma Shou-Feng. Comparison between the optimal velocity model and the Nagel-Schreckenberg model. Acta Physica Sinica, 2010, 59(2): 832-841. doi: 10.7498/aps.59.832
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    [9] Huang Ping-Hua, Tan Hui-Li, Liu Mu-Ren, Kong Ling-Jiang, Li Hua-Bing. A study on the traffic flow of the main road under the traffic light control. Acta Physica Sinica, 2003, 52(5): 1127-1131. doi: 10.7498/aps.52.1127
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  • Received Date:  07 September 2016
  • Accepted Date:  27 December 2016
  • Published Online:  05 May 2017

Stability analysis and fundamental diagram of heterogeneous traffic flow mixed with cooperative adaptive cruise control vehicles

    Corresponding author: Wang Hao, haowang@seu.edu.cn
  • 1. Jiangsu Key Laboratory of Urban ITS, School of Transportation, Southeast University, Nanjing 210096, China;
  • 2. Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Nanjing 210096, China;
  • 3. Guilin University of Electronic Technology, Guilin 541004, China;
  • 4. Hualan Design and Consulting Group, Nanning 530011, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 51478113, 51508122), the Foundation for Excellent Young Scientists of Southeast University, China (Grant No. 2242015R30028), and the Guangxi Science and Technology Project, China (Grant No. 15248002-10).

Abstract: This paper is aimed at building a framework for string stability analysis of traffic flow mixed with different cooperative adaptive cruise control (CACC) market penetration rates. In addition to the string stability, the fundamental diagram of the mixed flow is also taken into consideration for evaluating the effect of CACC vehicles on capacity. In order to describe the car-following dynamics of real CACC vehicles, the CACC model proposed by PATH is employed, which is validated by real experimental data. The intelligent driver model (IDM) is used as a surrogate car-following model for traditional manual driven vehicles. Based on the guidelines proposed by Ward[Ward J A 2009 Ph. D. Dissertation (Bristol:University of Bristol)], a framework is developed for the analytical investigation of heterogeneous traffic flow string stability. The framework presented considers the instability condition of traffic flow as a linear function of CACC market penetration rate. Following the framework, the string stabilities of the mixed traffic flow under different CACC market penetration rates and equilibrium velocities are analyzed. For fundamental diagram of the heterogeneous traffic flow, the equilibrium velocity-spacing functions of manual vehicles and CACC vehicles are obtained respectively based on car-following model. Then, the fundamental diagram of the density-velocity relationship of the heterogeneous traffic flow is derived based on the definition of traffic flow density. In addition, the theoretical fundamental diagram is plotted to show the property of traffic throughput. The numerical simulations are also carried out in order to investigate the effect of CACC vehicle on the characteristics of fundamental diagram. Besides, sensitivity analyses on CACC desired time gap are conducted for both string stability and fundamental diagram. Analytical studies and simulation results are as follows. 1) The heterogeneous traffic flow is stable for different equilibrium velocities and CACC market penetration rates, if manual driven vehicles are stable. Otherwise, the instability of traditional traffic flow is improved gradually with the increase of the CACC market penetration rate. Additionally, the stability will become better when equilibrium velocity is away from the velocity range of 9.6-18.6 m/s. 2) Because CACC vehicles can travel at free-flow speed in a relatively small headway, CACC vehicles can improve the capacity of heterogeneous traffic flow. 3) The results of sensitivity analysis indicate that with the increase of the CACC desired time gap, the stable region of heterogeneous traffic flow increases. However, the capacity of the fundamental diagram drops. Therefore, the value of the desired time gap should be determined with considering the effects of the two aspects on the heterogeneous traffic flow. It is noted that the CACC model used in this paper is based on the current state-of-the-art real CACC vehicle experiments. In the future, more experimental observations will yield new CACC models. However, the framework presented in this paper can still be used for the analytical investigation of string stability of the heterogeneous traffic flow at that time.

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