Fundamental Diagram and Stability Analysis of Heterogeneous Traffic Flow in a Connected and Autonomous Environment
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摘要:
为研究人工驾驶车辆和智能网联车辆（CAVs）的混合运行对交通流产生的影响，以其基本图和稳定性为突破口研究提高异质交通流运行效率的关键技术与方法。选择全速度差模型（FVDM）作为人工驾驶车辆跟驰模型，将加州伯克利分校实车数据标定的协同自适应巡航控制（CACC）模型作为CAVs跟驰模型。建立了异质交通流基本图模型，研究了CACC车辆的混入对道路通行能力的影响；对比了不同人工驾驶模型对异质流通行能力产生的差异性。从大车-小车组成的传统异质交通流研究方法入手，利用跟驰模型建立人工-网联异质流的稳定性解析方法，并运用Matlab验证了不同CACC比例下的稳定性分析。结果表明：与人工驾驶交通流相比，CACC同质交通流的道路通行能力大约提升了95%；实验中选用不同人工驾驶模型对通行能力实验结果造成的差异不大。平衡态速度为15 m/s时，低比例CAVs（如低于20%）并不能改善交通流；当CAVs比例达到20%及以上时，异质流稳定性随着CAVs的比例增加逐渐呈现出稳定趋势；当CAVs比例达到70%以上时，异质流基本稳定。
Abstract:This work focuses on the impacts of heterogeneous operation of manual driving vehicles and connected and autonomous vehicles(CAVs)on traffic flow. The fundamental diagram and stability of such traffic flow are set as the key technologies and methods to improve its operation. First, the full velocity difference model(FVDM)is selected as the car-following model of manual driving vehicles. Secondly, the cooperative adaptive cruise control(CACC)model calibrated with real-world vehicle location data from the University of California at Berkeley is used as the car-follow⁃ ing model of CAVs. Third, a fundamental diagram model of heterogeneous traffic flow is then developed to study the influence of CACC vehicles on road capacity and to compare the impacts of different manual driving models on hetero⁃ geneous flow capacity. In addition, based on the traditional research method of heterogeneous traffic flow consisting of vehicles of different sizes, the traditional car-following model is used to develop a stability analysis method for the het⁃ erogeneous traffic flow under study, and the stability analysis under different CACC ratios is carried out by Matlab. Study results confirms that, compared with the homogeneous manual-driving traffic flow, the road capacity under the homogeneous CACC traffic flow will be increased by about 95% and different manual driving models in the experiment has little impact onto the capacity. When the equilibrium speed is set at 15 m/s, a low proportion of CAVs(e.g. below 20%)won't improve the stability of traffic flow. On the other hand, when the proportion of CAVs reaches 20% and above, the heterogeneous flow gradually shows an increasing stable trend with an increased proportion of CAVs. It is al⁃ so found that, when the proportion of CAVs reaches 70% and above, traffic flow basically will maintain its stability.
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表 1 异质交通流的构成解析
Table 1. Analysis of the composition of heterogeneous traffic flow
序号 后车 前车 概率 退化后的跟随情况 1 人工驾驶车辆 人工驾驶车辆 SmSm 人工车辆跟随人工车辆 2 人工驾驶车辆 CACC车辆 SmSc 人工车辆跟随CACC车辆 3 CACC车辆 人工驾驶车辆 ScSm 人工车辆跟随人工车辆 4 CACC车辆 CACC车辆 Sc Sc CACC车辆跟随CACC车辆 注：Sm为人工驾驶车辆的实际数量比例，Sc为CACC车辆的实际数量比例（Sm + Sc = 1，Sm和Sc均在0~1之间）。 
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表 2 异质交通流的通行能力
Table 2. Capacity of heterogeneous traffic flow
CACC车辆比例Sc FVDM计算值/（veh/h） IDM计算值/（veh/h） 0 2 262 1 837 0.2 2 294 2 044 0.4 2 397 2 311 0.6 2 604 2 670 0.8 3 010 3 200 1 4 435 4 445
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表 3 异质交通流稳定性分析
Table 3. Stability analysis of heterogeneous traffic flow
CACC车辆比例Sc 稳定性计算值 稳定性上升值 0 -0.353 0 -- 0.1 -0.347 9 0.005 1 0.2 -0.332 6 0.015 3 0.3 -0.307 0 0.025 6 0.4 -0.271 3 0.035 7 0.5 -0.2253 0.046 0 0.6 -0.169 1 0.056 2 0.7 -0.102 7 0.066 4 0.8 -0.026 1 0.077 6 0.9 0.060 7 0.086 8 1 0.157 8 0.097 1
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