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摘要: 研究了高速交通中由于各种交通瓶颈而导致交通堵塞的过程, 通过与高速空气动力学中的激波问题作比拟, 建立适用于这一过程的交通流模型, 包括完全堵塞和部分堵塞两种状态下的不同模型。依据实际测量数据, 论证了平面交叉口绿灯转红灯时车流堵塞波的推进速度满足正态分布假设, 其拟合优度高于泊松分布假设。建立的完全堵塞状态下的交通流模型揭示, 随着上游来流的平均流量增加, 堵塞波的推进速度呈指数规律上升, 堵塞前后交通状态指数改变值在0.0 2~ 0.30范围内。根据部分堵塞状态下的交通流模型, 又可以得到不同程度堵塞条件下, 堵塞波的推进速度与上游来流流量之间的定量变化规律, 可以作为控制上游来流流量, 以减缓堵塞发展或尽快消除堵塞的计算依据。Abstract: The traffic flow modelling was established by shock wave simulation method. It is showed that a shock wave speed distribution in red light period at a plane intersection satisfies a normal assumption, as well as Poisson assumption. Based on completely jammed model, the wave speed increases as an exponential function of the traffic flow quantity. Traffic behavior parameter value may change 0 02~0 30 across the interrupted surface. The non-completely jammed model can calculate a control traffic quantity at upstream entrance of a bottleneck. 4 tabs, 8 refs.
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Key words:
- expressway /
- shock wave /
- traffic quantity /
- traffic flow modelling
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表 1 正态分布的假设检验
Table 1. Normal assumption examination
i xi/m·min-1 频数 Fk(xi) Pk(xi) Fk(xi)-Nk(xi) Fk(xi+1)-Nk(xi) 1 < 7 2 0.0333 0.0586 0.0253 0.0747 2 7~12 6 0.1333 0.1444 0.0110 0.1390 3 12~17 9 0.2833 0.2894 0.0060 0.2106 4 17~22 13 0.5000 0.4802 0.0198 0.2198 5 22~27 12 0.7000 0.6758 0.0242 0.1742 6 27~32 9 0.8500 0.8319 0.0181 0.0848 7 32~37 4 0.9167 0.9289 0.0122 0.0211 8 37~42 2 0.9500 0.9758 0.0258 0.0076 9 42~47 2 0.9833 0.9934 0.0101 0.0066 10 > 47 1 1.0000 0.9986 0.0014 0.0014 
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表 2 泊松分布的假设检验
Table 2. Poisson assumption examination
i xi/m·min-1 频数 Fk(xi) Pk(xi) Fk(xi)-Pk(xi) Fk(xi+1)-Pk(xi) 1 < 7 2 0.0333 0.0001 0.0332 0.1332 2 7~12 6 0.1333 0.0118 0.1215 0.2715 3 12~17 9 0.2833 0.1449 0.1384 0.3551 4 17~22 13 0.5000 0.5149 0.0149 0.1851 5 22~27 12 0.7000 0.8542 0.1542 0.0042 6 27~32 9 0.8500 0.9778 0.1278 0.0612 7 32~37 4 0.9167 0.9982 0.0816 0.0482 8 37~42 2 0.9500 0.9999 0.0499 0.0166 9 42~47 2 0.9833 1.0000 0.0167 0.0000 10 > 47 1 1.0000 1.0000 0.0000 0.0000
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表 3 N*与q1的函数拟合
Table 3. Function relationship between q1and N*
分组i 波速范围/m·min-1 平均波速N*/m·min-1 平均流量q1/veh·min-1 计算流量/veh·min-1 相对误差ε 1 < 4 3.3065 0.5600 0.5476 0.0221 2 4~9 7.1922 1.2292 1.2778 0.0396 3 9~14 11.8466 1.9713 2.0189 0.0241 4 14~19 16.1053 2.5813 2.5889 0.0030 5 19~24 21.1334 3.2397 3.1508 0.0275 6 24~29 26.2518 3.6427 3.6203 0.0061 7 > 29 34.4991 4.1709 4.2051 0.0082
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表 4 Δn(q1)函数值
Table 4. Function value of Δn(q1)
q1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Δn 0.026 0.052 0.079 0.105 0.132 0.159 0.187 0.215 0.243 0.271 0.299
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