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摘要: 通过实际观测和统计分析, 论证了平面交叉口红灯转绿灯时车流起动波速可以满足正态分布假设, 更可以满足泊松分布假设, 后者拟合优度高于前者。揭示了在周家嘴路条件下, 随着车辆排队长度增加, 起动波速会相应变大, 呈负指数规律上升的趋势, 与低速混合路段有明显差异。据此建议, 如将交通流动力学模型应用于高速公路或城市高架道路一类问题时, 状态指数取值在2.5左右为好。Abstract: In this paper, it is proved that the vehicle flow starting wave speed distribution in green light period at a plane intersection satisfies Poisson assumption as well as a normal assumption by actual observations and statistics analysis, and the Poisson assumption is better agreement with the observation data. It is also shown that with the increase of the vehicle flow queue length the starting wave speed will increase as a negative exponent function under the condition of Zhoujiazui road, which is obviously different from the roads in which vehicles run at low speed and together with bicycles. According to these results, it is proposed that the traffic behavior parameter in the traffic fluid dynamics model may be value about 2.5 in case of modeling of the expressway traffic procedures.
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表 1 周家嘴路车流起动波速频数分组情况
Table 1. Frequency numbers of vehicle flow starting wave speed of Zhoujiazui road
分组 起动波速/m·s-1 ≤3 4 5 6 7 8 9 10 11 ≥12 频数和 1 (dx≤30 m) 4 10 16 11 9 5 5 2 1 1 64 2 (32~38 m) 5 7 12 14 14 12 9 5 3 2 83 3 (40~46 m) 3 7 10 13 12 11 10 7 5 3 81 4 (48~54 m) 2 3 6 8 11 9 6 5 3 2 55 5 (dx≥56 m) 0 1 4 6 6 7 5 2 2 1 34 6 (合计) 14 28 48 52 52 44 35 21 14 9 317 
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表 2 测量数据的计算结果
Table 2. Calculation results of measurement data
分组编号 样本容量N 起动波速平均值μ/m·s-1 标准方差σ/m·s-1 平均排队长度L/m 1 64 6.08 2.026 28.4 2 83 6.86 2.193 36.0 3 81 7.26 2.312 43.4 4 55 7.45 2.107 50.4 5 34 7.56 1.926 61.6 6 317 6.97 2.209 41.6
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表 3 分组编号1样本服从正态分布的假设检验
Table 3. Normal assumption examination for the sample group 1
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) < 3.5 4 0.0625 0.0621 0.0004 0.1567 [3.5, 4.5) 10 0.2188 0.1785 0.0403 0.2903 [4.5, 5.5) 16 0.4688 0.3494 0.1194 0.2913 [5.5, 6.5) 11 0.6406 0.5461 0.0945 0.2351 [6.5, 7.5) 9 0.7813 0.7237 0.0576 0.1357 [7.5, 8.5) 5 0.8594 0.8492 0.0101 0.0883 [8.5, 9.5) 5 0.9375 0.9188 0.0187 0.0499 [9.5, 10.5) 2 0.9688 0.9491 0.0197 0.0353 [10.5, 11.5) 1 0.9844 0.9594 0.0250 0.0406 ≥11.5 1 1 0.9621 0.0379 0.0379
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表 4 分组编号2样本服从正态分布的假设检验
Table 4. Normal assumption examination for the sample group 2
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) < 3.5 5 0.0602 0.0388 0.0215 0.1058 [3.5, 4.5) 7 0.1446 0.1167 0.0279 0.1724 [4.5, 5.5) 12 0.2892 0.2439 0.0453 0.2139 [5.5, 6.5) 14 0.4578 0.4125 0.0453 0.2140 [6.5, 7.5) 14 0.6265 0.5940 0.0325 0.1770 [7.5, 8.5) 12 0.7711 0.7528 0.0183 0.1267 [8.5, 9.5) 9 0.8795 0.8656 0.0139 0.0742 [9.5, 10.5) 5 0.9398 0.9306 0.0091 0.0453 [10.5, 11.5) 3 0.9759 0.9611 0.0148 0.0389 ≥11.5 2 1 0.9727 0.0273 0.0273
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表 5 分组编号3样本服从正态分布的假设检验
Table 5. Normal assumption examination for the sample group 3
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) < 3.5 3 0.0370 0.0316 0.0054 0.0918 [3.5, 4.5) 7 0.1235 0.0955 0.0280 0.1514 [4.5, 5.5) 10 0.2469 0.2025 0.0444 0.2049 [5.5, 6.5) 13 0.4074 0.3513 0.0561 0.2042 [6.5, 7.5) 12 0.5556 0.5228 0.0328 0.1686 [7.5, 8.5) 11 0.6914 0.6867 0.0046 0.1281 [8.5, 9.5) 10 0.8148 0.8167 0.0019 0.0845 [9.5, 10.5) 7 0.9012 0.9022 0.0009 0.0608 [10.5, 11.5) 5 0.9630 0.9488 0.0142 0.0512 ≥11.5 3 1 0.9698 0.0302 0.0302
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表 6 分组编号4样本服从正态分布的假设检验
Table 6. Normal assumption examination for the sample group 4
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) < 3.5 2 0.0364 0.0246 0.0118 0.0663 [3.5, 4.5) 3 0.0909 0.0799 0.0110 0.1201 [4.5, 5.5) 6 0.2000 0.1807 0.0193 0.1647 [5.5, 6.5) 8 0.3455 0.3300 0.0154 0.2154 [6.5, 7.5) 11 0.5455 0.5094 0.0360 0.1966 [7.5, 8.5) 9 0.7091 0.6845 0.0246 0.1337 [8.5, 9.5) 6 0.8182 0.8231 0.0050 0.0859 [9.5, 10.5) 5 0.9091 0.9123 0.0032 0.0513 [10.5, 11.5) 3 0.9636 0.9588 0.0048 0.0412 ≥11.5 2 1 0.9785 0.0215 0.0215
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表 7 分组编号5样本服从正态分布的假设检验
Table 7. Normal assumption examination for the sample group 5
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) < 3.5 0 0.0000 0.0126 0.0126 0.0168 [3.5, 4.5) 1 0.0294 0.0501 0.0207 0.0969 [4.5, 5.5) 4 0.1471 0.1358 0.0112 0.1877 [5.5, 6.5) 6 0.3235 0.2851 0.0384 0.2149 [6.5, 7.5) 6 0.5000 0.4837 0.0163 0.2222 [7.5, 8.5) 7 0.7059 0.6855 0.0204 0.1674 [8.5, 9.5) 5 0.8529 0.8421 0.0109 0.0697 [9.5, 10.5) 2 0.9118 0.9349 0.0231 0.0357 [10.5, 11.5) 2 0.9706 0.9768 0.0062 0.0232 ≥11.5 1 1 0.9913 0.0087 0.0087
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表 8 分组编号6样本服从正态分布的假设检验
Table 8. Normal assumption examination for the sample group 6
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) < 3.5 14 0.0442 0.0360 0.0082 0.0965 [3.5, 4.5) 28 0.1325 0.1092 0.0233 0.1747 [4.5, 5.5) 48 0.2839 0.2306 0.0533 0.2174 [5.5, 6.5) 52 0.4480 0.3947 0.0533 0.2173 [6.5, 7.5) 52 0.6120 0.5752 0.0367 0.1755 [7.5, 8.5) 44 0.7508 0.7372 0.0136 0.1240 [8.5, 9.5) 35 0.8612 0.8555 0.0057 0.0719 [9.5, 10.5) 21 0.9274 0.9259 0.0015 0.0457 [10.5, 11.5) 14 0.9716 0.9601 0.0115 0.0399 ≥11.5 9 1 0.9736 0.0264 0.0264
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表 9 分组编号1样本服从泊松分布的假设检验
Table 9. Poisson & apos; s assumption examination for the sample group 1
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) 3 4 0.0625 0.0858 0.0233 0.1330 4 10 0.2188 0.2162 0.0026 0.2528 5 16 0.4688 0.3746 0.0941 0.2660 6 11 0.6406 0.5352 0.1054 0.2461 7 9 0.7813 0.6746 0.1067 0.1848 8 5 0.8594 0.7805 0.0789 0.1570 9 5 0.9375 0.8520 0.0855 0.1167 10 2 0.9688 0.8955 0.0733 0.0889 11 1 0.9844 0.9195 0.0649 0.0805 12 1 1 0.9317 0.0683 0.0683
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表 10 分组编号2样本服从泊松分布的假设检验
Table 10. Poisson & apos; s assumption examination for the sample group 2
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) 3 5 0.0602 0.0566 0.0037 0.0880 4 7 0.1446 0.1536 0.0090 0.1356 5 12 0.2892 0.2865 0.0026 0.1713 6 14 0.4578 0.4384 0.0194 0.1881 7 14 0.6265 0.5872 0.0393 0.1839 8 12 0.7111 0.7147 0.0564 0.1648 9 9 0.8795 0.8118 0.0677 0.1279 10 5 0.9398 0.8784 0.0614 0.0975 11 3 0.9759 0.9199 0.0560 0.0801 12 2 1 0.9436 0.0564 0.0564
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表 11 分组编号3样本服从泊松分布的假设检验
Table 11. Poisson & apos; s assumption examination for the sample group 3
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) 3 3 0.0370 0.0449 0.0078 0.0786 4 7 0.1235 0.1263 0.0028 0.1206 5 10 0.2469 0.2445 0.0024 0.1629 6 13 0.4074 0.3875 0.0199 0.1681 7 12 0.5556 0.5358 0.0198 0.1556 8 11 0.6914 0.6704 0.0210 0.1444 9 10 0.8148 0.7789 0.0359 0.1223 10 7 0.9012 0.8577 0.0435 0.1053 11 5 0.9630 0.9097 0.0533 0.0903 12 3 1 0.9412 0.0588 0.0588
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表 12 分组编号4样本服从泊松分布的假设检验
Table 12. Poisson & apos; s assumption examination for the sample group 4
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) 3 2 0.0364 0.0417 0.0054 0.0492 4 3 0.0909 0.1187 0.0278 0.0813 5 6 0.2000 0.2324 0.0324 0.1130 6 8 0.3455 0.3723 0.0269 0.1731 7 11 0.5455 0.5198 0.0256 0.1893 8 9 0.7091 0.6560 0.0531 0.1622 9 6 0.8182 0.7676 0.0506 0.1415 10 5 0.9091 0.8500 0.0591 0.1136 11 3 0.9636 0.9053 0.0583 0.0947 12 2 1 0.9393 0.0607 0.0607
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表 13 分组编号5样本服从泊松分布的假设检验
Table 13. Poisson & apos; s assumption examination for the sample group 5
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) 3 0 0.0000 0.0375 0.0375 0.0081 4 1 0.0294 0.1085 0.0791 0.0386 5 4 0.1471 0.2157 0.0686 0.1078 6 6 0.3235 0.3508 0.0273 0.1492 7 6 0.5000 0.4968 0.0033 0.2092 8 7 0.7059 0.6345 0.0714 0.2184 9 5 0.8529 0.7503 0.1027 0.1615 10 2 0.9118 0.8378 0.0740 0.1328 11 2 0.9706 0.8979 0.0277 0.1021 12 1 1 0.9358 0.0642 0.0642
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表 14 分组编号6样本服从泊松分布的假设检验
Table 14. Poisson & apos; s assumption examination for the sample group 6
起动波速 频数 Fk (xi) F0 (xi) Fk (xi) -F0 (xi) Fk (xi+1) -F0 (xi) 3 14 0.0442 0.0531 0.0089 0.0794 4 28 0.1325 0.1455 0.0130 0.1384 5 48 0.2839 0.2774 0.0095 0.1735 6 52 0.4480 0.4241 0.0239 0.1879 7 52 0.6120 0.5731 0.0389 0.1777 8 44 0.7508 0.7028 0.0479 0.1584 9 35 0.8612 0.8033 0.0579 0.1241 10 21 0.9274 0.8734 0.0541 0.0983 11 14 0.9716 0.9177 0.0539 0.0823 12 9 1 0.9435 0.0565 0.0565
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表 15 正态分布和泊松分布拟合优度对比
Table 15. Contrast of imitation degree between normal and Poisson' s assumption
分组编号 1 2 3 4 5 6 正态分布 0.2913 0.2140 0.2049 0.2154 0.2222 0.2174 泊松分布 0.2660 0.1881 0.1681 0.1893 0.2184 0.1879
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[1] WU Zheng. Traffic flow dynamic modeling[J]. Journal of Fudan University(Natural Science), 1991, 30(1): 111-117. [2] WU Zheng. Measurement and analysis for dynamic modeling of traffic flows[J]. Journal of Fudan University(Natural Science), 1991, 30(2): 224-230. [3] WU Zheng. A fluid dynamic model for the low speed traffic system[J]. Acta Mechanica Sinica, 1994, 26(2): 149-157. [4] 薛珊荣, 等. 城市交通工程与街道规划设计[M]. 北京: 中国建筑工业出版社, 1988. [5] 苏均和. 概率与数理统计[M]. 上海: 上海财经大学出版社, 1999. -
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