网联车混合交通流渐进稳定性解析方法
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摘要
针对网联车与普通车构成的混合交通流不稳定性问题,提出一种网联车混合交通流渐进稳定性解析方法.基于传递函数理论,应用跟驰模型推导扰动在交通流中传播时的传递函数,并建立不同网联车比例下的混合交通流渐进稳定性解析框架.选取智能驾驶模型(intelligent driver model, IDM)与优化速度模型(optimal velocity model,OVM)分别作为网联车与普通车的跟驰模型,进行混合交通流渐进稳定性案例分析,并进行小扰动下的数值仿真.研究结果表明:所建立的混合交通流渐进稳定性解析框架可计算得到关于网联车比例与平衡态速度的混合交通流稳定域;当平衡态速度大于21.5 m/s时,混合交通流可在任意网联车比例下稳定,当网联车比例大于0.63时,混合交通流可在任意平衡态速度下稳定;混合交通流稳定性数值仿真实验验证了理论解析的正确性.所建立的网联车混合交通流渐进稳定性解析框架适用于不同跟驰模型的选取,能够用于分析真车实验条件下网联车对交通流稳定性的影响.
Focusing on the instability of mixed traffic flow including connected vehicles and traditional vehicles, this paper proposes an analytical method for the asymptotic stability of the mixed traffic flow with connected vehicles. Based on the transfer function theory, the car-following models were used to derive the transfer function of disturbances spreading in traffic flow. Then the analytical framework of asymptotic stability of mixed traffic flow was built under different proportions of connected vehicles. The intelligent driver model(IDM) and optimal velocity model(OVM) were selected as car-following models for connected vehicles and traditional vehicles, respectively. Subsequently, case analysis of asymptotic stability of mixed traffic flow was conducted and numerical simulations were performed under small disturbances. Results showed that the proposed analytical framework of asymptotic stability of the mixed traffic flow can be used to calculate the stability region of the mixed traffic flow related to connected vehicle proportion and equilibrium velocity. When the equilibrium velocity was larger than 21.5 m·s~(-1), the mixed traffic flow was stable under any connected vehicle proportion. When the connected vehicle proportion was larger than 0.63, the mixed traffic flow was stable under any equilibrium velocity. Moreover, the numerical simulation experiments of mixed traffic flow validated the soundness of the theoretical analysis. The analytical framework of asymptotic stability of mixed traffic flow can be applied to different car-following models. It can also be used to analyze impacts of connected vehicles on traffic flow stability under the condition of real experimental tests.
Focusing on the instability of mixed traffic flow including connected vehicles and traditional vehicles, this paper proposes an analytical method for the asymptotic stability of the mixed traffic flow with connected vehicles. Based on the transfer function theory, the car-following models were used to derive the transfer function of disturbances spreading in traffic flow. Then the analytical framework of asymptotic stability of mixed traffic flow was built under different proportions of connected vehicles. The intelligent driver model(IDM) and optimal velocity model(OVM) were selected as car-following models for connected vehicles and traditional vehicles, respectively. Subsequently, case analysis of asymptotic stability of mixed traffic flow was conducted and numerical simulations were performed under small disturbances. Results showed that the proposed analytical framework of asymptotic stability of the mixed traffic flow can be used to calculate the stability region of the mixed traffic flow related to connected vehicle proportion and equilibrium velocity. When the equilibrium velocity was larger than 21.5 m·s~(-1), the mixed traffic flow was stable under any connected vehicle proportion. When the connected vehicle proportion was larger than 0.63, the mixed traffic flow was stable under any equilibrium velocity. Moreover, the numerical simulation experiments of mixed traffic flow validated the soundness of the theoretical analysis. The analytical framework of asymptotic stability of mixed traffic flow can be applied to different car-following models. It can also be used to analyze impacts of connected vehicles on traffic flow stability under the condition of real experimental tests.
引文
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[3] TANG T Q, CHEN L, YANG S C, et al. An extended car-following model with consideration of the electric vehicle’s driving range[J]. Physica A: Statistical Mechanics and Its Applications, 2015, 430: 148
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[8] WARD J A. Heterogeneity, lane-changing and instability in traffic: A mathematical approach[D].Bristol: University of Bristol, 2009
[9] TALEBPOUR A, MAHMASSANI H S. Influence of connected and autonomous vehicles on traffic flow stability and throughput[J]. Transportation Research Part C: Emerging Technologies, 2016, 71: 143
[10]秦严严, 王昊. 智能网联车辆交通流优化对交通安全的改善[J]. 中国公路学报, 2018, 31(4): 202 QIN Yanyan, WANG Hao. Improving traffic safety via traffic flow optimization of connected and automated vehicles[J].China Journal of Highway and Transport, 2018, 31(4): 202
[11]KONISHI K, KOKAME H, HIRATA K. Decentralized delayed-feedback control of an optimal velocity traffic model[J]. The European Physical Journal B:Condensed Matter and Complex Systems, 2000, 15(4): 715
[12]NAUS G J L, VUGTS R P A, PLOEG J, et al. String-stable CACC design and experimental validation: a frequency-domain approach[J]. IEEE Transactions on Vehicular Technology, 2010, 59(9): 4268
[13]GE J I, OROSZ G. Dynamics of connected vehicle systems with delayed acceleration feedback[J]. Transportation Research Part C: Emerging Technologies, 2014, 46: 46
[14]秦严严, 王昊, 王炜, 等. 混有CACC车辆和ACC车辆的异质交通流基本图模型[J]. 中国公路学报, 2017, 30(10): 127 QIN Yanyan, WANG Hao, WANG Wei, et al. Fundamental diagram of heterogeneous traffic flow mixed with cooperative adaptive cruise control vehicles and adaptive cruise control vehicles [J].China Journal of Highway and Transport, 2017, 30(10): 127
[15]WANG H, WANG W, CHEN J, et al. Estimating equilibrium speed-spacing relationship from dynamic trajectory data[C]// Proceedings of the 91st Annual Meeting of the Transportation Research Board.Washington DC: TRB, 2012: 1
[2] 秦严严, 王昊, 王炜, 等. 自适应巡航控制车辆跟驰模型综述. 交通运输工程学报, 2017, 17(3): 121 QIN Yanyan, WANG Hao, WANG Wei, et al. Review of car-following models of adaptive cruise control[J]. Journal of Traffic and Transportation Engineering, 2017, 17(3): 121
[3] TANG T Q, CHEN L, YANG S C, et al. An extended car-following model with consideration of the electric vehicle’s driving range[J]. Physica A: Statistical Mechanics and Its Applications, 2015, 430: 148
[4] PUEBOOBPAPHAN R, VAN AREM B. Driver and vehicle characteristics and platoon and traffic flow stability: Understanding the relationship for design and assessment of cooperative adaptive cruise control[J]. Transportation Research Record: Journal of the Transportation Research Board, 2010 (2189): 89
[5] LI P Y, SHRIVASTAVA A. Traffic flow stability induced by constant time headway policy for adaptive cruise control vehicles[J]. Transportation Research Part C: Emerging Technologies, 2002, 10(4): 275
[6] LI Z, LI W, XU S, et al. Stability analysis of an extended intelligent driver model and its simulations under open boundary condition[J]. Physica A: Statistical Mechanics and Its Applications, 2015, 419: 526
[7] HOLLAND E N. A generalised stability criterion for motorway traffic[J]. Transportation Research Part B: Methodological, 1998, 32(2): 141
[8] WARD J A. Heterogeneity, lane-changing and instability in traffic: A mathematical approach[D].Bristol: University of Bristol, 2009
[9] TALEBPOUR A, MAHMASSANI H S. Influence of connected and autonomous vehicles on traffic flow stability and throughput[J]. Transportation Research Part C: Emerging Technologies, 2016, 71: 143
[10]秦严严, 王昊. 智能网联车辆交通流优化对交通安全的改善[J]. 中国公路学报, 2018, 31(4): 202 QIN Yanyan, WANG Hao. Improving traffic safety via traffic flow optimization of connected and automated vehicles[J].China Journal of Highway and Transport, 2018, 31(4): 202
[11]KONISHI K, KOKAME H, HIRATA K. Decentralized delayed-feedback control of an optimal velocity traffic model[J]. The European Physical Journal B:Condensed Matter and Complex Systems, 2000, 15(4): 715
[12]NAUS G J L, VUGTS R P A, PLOEG J, et al. String-stable CACC design and experimental validation: a frequency-domain approach[J]. IEEE Transactions on Vehicular Technology, 2010, 59(9): 4268
[13]GE J I, OROSZ G. Dynamics of connected vehicle systems with delayed acceleration feedback[J]. Transportation Research Part C: Emerging Technologies, 2014, 46: 46
[14]秦严严, 王昊, 王炜, 等. 混有CACC车辆和ACC车辆的异质交通流基本图模型[J]. 中国公路学报, 2017, 30(10): 127 QIN Yanyan, WANG Hao, WANG Wei, et al. Fundamental diagram of heterogeneous traffic flow mixed with cooperative adaptive cruise control vehicles and adaptive cruise control vehicles [J].China Journal of Highway and Transport, 2017, 30(10): 127
[15]WANG H, WANG W, CHEN J, et al. Estimating equilibrium speed-spacing relationship from dynamic trajectory data[C]// Proceedings of the 91st Annual Meeting of the Transportation Research Board.Washington DC: TRB, 2012: 1
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