基于交通流生存函数的交叉口通行能力计算模型

胡尧; 韦维; 商明菊; 李丽; 李扬

doi:10.19818/j.cnki.1671-1637.2019.04.013

基于交通流生存函数的交叉口通行能力计算模型

doi: 10.19818/j.cnki.1671-1637.2019.04.013

胡尧^{1, 2,},
韦维^{1, 3},
商明菊¹,
李丽¹,
李扬¹

1.
贵州大学数学与统计学院, 贵州贵阳 550025
2.
贵州大学贵州省公共大数据重点实验室, 贵州贵阳 550025
3.
贵州民族大学数据科学与信息工程学院, 贵州贵阳 550025

基金项目:

国家自然科学基金项目 11661018

贵州省科技计划项目黔科合平台人才[2017]5788号

全国统计科学研究项目 2014LZ46

贵州省科学技术基金项目黔科合J字[2014]2058号

详细信息

作者简介:
胡尧(1971-), 男, 贵州遵义人, 贵州大学教授, 从事城市道路交通问题与应用统计研究

中图分类号: U491.14
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- 被引次数: 0
出版历程
- 收稿日期: 2019-03-18
- 刊出日期: 2019-08-25

Calculation model of intersection capacity based on traffic flow survival function

HU Yao^{1, 2
,},
WEI Wei^{1, 3},
SHANG Ming-ju¹,
LI Li¹,
LI Yang¹

1.
School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China
2.
Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, Guizhou, China
3.
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, Guizhou, China

More Information

Author Bio:
HU Yao(1971-), male, professor, yhu1@gzu.edu.cn

摘要

摘要: 针对基本通行能力不能全面反映道路交通状况的缺点, 提出了城市道路随机化通行能力概念; 依据评价体系定义交通中断与持续中断, 量化了城市道路交通拥堵程度; 研究了现有通行能力估计方法, 利用乘积限与寿命分布列构造并估计了交通流分布函数; 结合交叉口各入口交通流数据特性改进传统连续交通流参数模型, 提出了基于交通流生存函数的交叉口通行能力计算模型; 将该模型估计结果与道路通行能力手册HCM2010中的模型估计结果和交叉口实测流量进行误差对比。分析结果表明: 生存函数模型计算出的中断、持续中断交叉口通行能力与HCM2010中的模型计算结果误差均值分别为0.162 1与0.116 4, 方差分别为0.029 0与0.015 2, 两者误差波动均较小; 提出的计算模型结果与实测较大流量相对误差分别为9.720%、3.822%和4.936%、4.779%, 统计意义下提出的计算模型相对误差为5.871%, 估计效果稳健; 城市道路交通中断次数、可接受中断概率、交通流、速度与道路通行能力之间存在生存函数乘积限对应关系, 研究交叉口的通行能力为7 632 pcu·h^-1, 提出的计算模型估计结果更具有可靠性。可见, 提出的计算模型适用性较好, 特别在不同拥堵程度的城市道路交通区域, 通过可接受中断概率估计通行能力, 可为城市道路交通组织与管理部门提供优化目标、科学决策和易于接受的理论依据。
- 通行能力 /
- 生存函数 /
- 交通流 /
- 乘积限 /
- 交通中断
Abstract: The concept of stochastic traffic capacity of urban road was proposed for the disadvantage that the basic traffic capacity was unable to fully reflect the road traffic conditions. According to the evaluation system, the traffic breakdown and continuous breakdown were defined to quantify the degree of urban road traffic congestion. The existing estimation methods of traffic capacity were studied, and the product-limit and lifetime distribution were used to construct and estimate the traffic flow distribution function. The parameter model of traditional continuous traffic flow was improved by combining the characteristics of traffic flow data of each intersection entrance, and a calculation model of intersection capacity based on traffic flow survival function was proposed. The estimation result of the calculation model was compared with Highway Capacity Manual 2010 model and practical traffic flow of intersection to analyze the computation errors. Analysis result shows that the mean errors of intersection capacity with traffic breakdown and continuous breakdown calculated by the survival function model and HCM2010 model are 0.162 1 and 0.116 4, respectively, and the variances are 0.029 0 and 0.015 2, respectively, both have small error fluctuation. The relative errors between the results of the proposed calculation model and the measured greater traffic flow are 9.720%, 3.822% and 4.936%, 4.779%, respectively. The relative error of the proposed calculation model in a statistic sense is 5.871%, and the estimation effect is robust. There is a product-limit survival function between the traffic breakdown time, probability of acceptable breakdown, traffic flow, speed and traffic capacity. The traffic capacity of the researched intersection is 7 632 pcu·h^-1, so the estimation result of the proposed calculation model is more reliable. Therefore, the proposed calculation model has high practicability, especially in urban road traffic areas with different congestion degrees. By estimating traffic capacity of the acceptable breakdown probability, the optimization objective, scientific decision and acceptable theoretical basis can be provided for urban road traffic organization and management department.
- traffic capacity /
- survival function /
- traffic flow /
- product-limit /
- traffic breakdown

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图 1 交叉口线圈检测交通流数据

Figure 1. Detect traffic flow data from intersection coil

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图 2 流量时序

Figure 2. Time series of traffic flow

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图 3 速度时序

Figure 3. Time series of speed

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图 4 持续中断前后交叉口各入口车道车速

Figure 4. Speeds before and after continuous breakdown for entry lane of intersection

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图 5 HCM2010中的模型与2种中断定义的拟合曲线

Figure 5. Fitting curves of HCM2010 model and two kinds of breakdown definitions

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图 6 HCM2010中的模型与2种中断定义的生存函数估计曲线

Figure 6. Estimating curves of survival function based on HCM2010 model and two kinds of breakdown definitions

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图 7 模型通行能力估计值与实测流量

Figure 7. Model capacity estimations and measured traffic flow

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表 1 高峰时段城市主干道平均车速分级

Table 1. Average speed rating scales of urban main roads in peak period

评价标准等级	一	二	三	四	五
大型城市/ (km·h^-1)	≥25	[22, 25)	[19, 22)	[16, 19)	[0, 16)
中型城市/ (km·h^-1)	≥28	[25, 28)	[22, 25)	[19, 22)	[0, 19)
小型城市/ (km·h^-1)	≥30	[27, 30)	[24, 27)	[21, 24)	[0, 21)

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表 2 交通中断前后车速统计结果

Table 2. Statistics results of speed before and after traffic breakdown

入口方向	中断次数	统计时刻	25%分位数/ (km·h^-1)	中位数/ (km·h^-1)	均值/ (km·h^-1)	75%分位数/ (km·h^-1)	标准差/ (km·h^-1)	最小值/ (km·h^-1)	最大值/ (km·h^-1)
东	2 622	中断前	24.565 6	26.808 0	27.615 6	29.691 8	4.190 3	22.055 0	40.000 0
东	2 622	中断后	4.772 5	6.837 3	7.645 1	10.154 7	3.627 5	0.962 3	15.856 8
南	1 524	中断前	24.891 8	27.872 4	28.849 3	32.429 3	4.898 5	22.044 2	40.000 0
南	1 524	中断后	6.684 6	9.828 8	9.460 4	12.352 7	3.888 5	1.023 7	15.663 6
西	2 635	中断前	24.039 3	25.934 9	26.589 6	28.437 4	3.358 5	22.023 5	40.000 0
西	2 635	中断后	6.356 0	8.305 4	8.638 6	10.580 2	3.139 7	1.463 0	15.848 9
北	1 485	中断前	25.330 8	28.717 8	29.398 1	33.011 8	4.884 4	22.483 8	40.000 0
北	1 485	中断后	6.562 0	9.780 0	9.525 0	12.617 9	3.921 5	1.438 0	15.732 3

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表 3 交通中断前后流量统计结果

Table 3. Statistics results of traffic flow before and after traffic breakdown

入口方向	中断次数	统计时刻	25%分位数/pcu	中位数/pcu	均值/pcu	75%分位数/pcu	标准差/pcu	最小值/pcu	最大值/pcu
东	2 622	中断前	20.500 0	27.500 0	27.422 7	33.500 0	10.012 5	7.000 0	59.000 0
东	2 622	中断后	20.000 0	26.250 0	25.702 0	31.000 0	8.743 7	2.750 0	56.750 0
南	1 524	中断前	14.708 3	17.916 7	18.250 7	21.500 0	5.190 8	7.166 7	33.500 0
南	1 524	中断后	10.708 3	14.500 0	15.118 7	19.333 3	5.954 6	0.666 7	32.500 0
西	2 635	中断前	20.000 0	26.250 0	25.667 1	31.562 5	8.975 9	7.000 0	53.750 0
西	2 635	中断后	19.250 0	25.000 0	24.162 1	29.250 0	8.078 5	2.500 0	48.250 0
北	1 485	中断前	18.791 7	26.666 7	26.195 8	31.625 0	8.819 3	11.166 7	58.333 3
北	1 485	中断后	14.833 3	22.166 7	21.563 9	26.500 0	7.934 9	5.833 3	42.500 0

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表 4 交通中断定义下交叉口各入口方向通行能力估计结果

Table 4. Estimation results of capacity for entry directions of intersection under traffic breakdown

入口方向	车道序号	I_j= (b_j-1, b_j]	N_j	d_j	$\overset{\land}{q} (j)$	$\overset{\land}{p} = 1 - \overset{\land}{q} (j)$	$\overset{\land}{Ρ} (j)$	20%估计值	20%期望估计值	估计值汇总	期望估计值汇总
东	1	(30, 34]	384	31	0.080 7	0.919 3	0.832 5	38	35	142	133
	1	(34, 38]	353	33	0.093 5	0.906 5	0.754 7	38	35
	2	(30, 34]	388	27	0.069 6	0.930 4	0.849 4	42	38
	2	(34, 38]	361	36	0.099 7	0.900 3	0.764 7	42	38
	3	(26, 31]	830	119	0.143 4	0.856 6	0.800 7	31	30
	3	(31, 36]	711	162	0.227 8	0.772 2	0.618 2	31	30
	4	(26, 31]	830	117	0.141 0	0.859 0	0.805 6	31	30
	4	(31, 36]	713	161	0.225 8	0.774 2	0.623 7	31	30
南	5	(14, 16]	89	7	0.078 6	0.921 3	0.836 7	18	17	122	115
	5	(16, 18]	82	11	0.134 1	0.865 9	0.724 5	18	17
	6	(12, 14]	88	7	0.079 6	0.920 5	0.835 1	19	16
	6	(14, 16]	81	9	0.111 1	0.888 9	0.742 3	19	16
	7	(14, 16]	370	17	0.046 0	0.954 1	0.912 1	20	19
	7	(16, 18]	353	36	0.102 0	0.898 0	0.819 1	20	19
	8	(21, 24]	500	49	0.098 0	0.902 0	0.823 0	24	23
	8	(24, 27]	451	109	0.241 7	0.758 3	0.624 1	24	23
	9	(15, 18]	247	24	0.097 2	0.902 8	0.874 5	18	18
	9	(18, 21]	223	48	0.215 2	0.784 8	0.686 3	18	18
	10	(15, 23]	137	21	0.153 3	0.846 7	0.834 5	23	22
	10	(23, 31]	116	42	0.362 1	0.637 9	0.532 4	23	22
西	11	(26, 31]	317	24	0.075 7	0.924 3	0.874 6	36	34	133	126
	11	(31, 36]	293	52	0.177 5	0.822 5	0.719 4	36	34
	12	(24, 30]	872	7	0.008 0	0.992 0	0.985 2	42	40
	12	(30, 36]	865	38	0.043 9	0.956 1	0.941 9	42	40
	13	(18, 24]	366	28	0.076 5	0.923 5	0.896 6	24	23
	13	(24, 30]	338	87	0.257 4	0.742 6	0.665 8	24	23
	14	(21, 26]	1 003	61	0.060 8	0.939 2	0.901 4	31	29
	14	(26, 31]	942	128	0.135 9	0.864 1	0.778 9	31	29
北	15	(21, 26]	57	6	0.105 3	0.894 7	0.836 1	26	25	239	223
	15	(26, 31]	51	16	0.313 7	0.686 3	0.573 8	26	25
	16	(37, 43]	16	2	0.125 0	0.875 0	0.823 5	49	44
	16	(43, 49]	14	2	0.142 9	0.857 1	0.705 9	49	44
	17	(26, 31]	374	47	0.125 7	0.874 3	0.840 6	31	30
	17	(31, 36]	327	121	0.370 0	0.630 0	0.529 6	31	30
	18	(83, 90]	458	73	0.159 4	0.840 6	0.805 4	90	88
	18	(90, 97]	385	148	0.384 4	0.615 6	0.495 8	90	88
	19	(18, 22]	483	52	0.107 7	0.892 3	0.838 5	22	21
	19	(22, 26]	431	123	0.285 4	0.714 6	0.599 2	22	21
	20	(0, 10]	26	2	0.076 9	0.923 1	0.923 1	21	15
	20	(10, 14]	26	4	0.166 7	0.833 3	0.769 2	21	15
合计	中断定义下的信号交叉口5 min流量估计值/pcu									636	597
合计	中断定义下的信号交叉口通行能力估计值/ (pcu·h^-1)									7 632	7 164

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表 5 持续中断前后车速统计结果

Table 5. Statistics results of speed before and after continuous breakdown

入口方向	中断次数	统计时刻	25%分位数/ (km·h^-1)	中位数/ (km·h^-1)	均值/ (km·h^-1)	75%分位数/ (km·h^-1)	标准差/ (km·h^-1)	最小值/ (km·h^-1)	最大值/ (km·h^-1)
东	1 711	中断前	24.338 9	26.501 3	27.301 2	29.230 3	3.955 4	22.063 3	40.000 0
		中断后	4.527 2	6.309 5	7.114 1	9.120 3	3.445 4	0.962 3	15.829 9
		下一间隔	4.417 8	6.650 3	7.225 6	9.550 4	3.408 5	0.000 0	15.958 8
南	704	中断前	23.995 3	26.257 2	27.026 2	29.721 8	3.822 1	22.044 2	35.938 7
		中断后	4.866 2	8.043 7	8.303 3	11.427 0	4.219 9	1.356 2	15.535 9
		下一间隔	5.950 5	9.018 1	9.055 2	11.850 9	3.809 9	2.824 9	15.559 0
西	1 529	中断前	24.090 5	25.831 5	26.533 0	28.348 3	3.291 9	22.093 8	39.183 4
		中断后	6.267 0	8.190 9	8.467 5	10.262 8	3.146 3	1.600 4	15.832 0
		下一间隔	6.012 7	8.061 5	8.349 3	10.365 2	3.271 3	1.104 3	15.763 1
北	751	中断前	28.555 4	32.785 0	33.371 9	37.320 4	5.617 0	26.613 1	40.000 0
		中断后	6.383 0	10.137 2	9.782 3	12.789 6	4.592 2	1.953 6	17.677 6
		下一间隔	5.912 6	9.106 3	9.520 8	12.876 5	4.145 3	2.537 9	17.347 0

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表 6 持续中断前后流量统计结果

Table 6. Statistics results of traffic flow before and after continuous breakdown

入口方向	中断次数	统计时刻	25%分位数/pcu	中位数/pcu	均值/pcu	75%分位数/pcu	标准差/pcu	最小值/pcu	最大值/pcu
东	1 711	中断前	23.312 5	29.625 0	29.422 6	35.500 0	9.220 1	8.250 0	59.000 0
		中断后	23.000 0	27.250 0	27.245 6	31.750 0	7.859 9	5.250 0	56.750 0
		下一间隔	23.062 5	28.500 0	28.115 0	33.187 5	7.950 2	0.000 0	55.250 0
南	704	中断前	14.333 3	17.666 7	18.144 7	21.208 3	5.265 4	7.166 7	31.833 3
		中断后	10.541 7	14.833 3	15.086 3	19.125 0	6.104 5	1.166 7	27.833 3
		下一间隔	11.750 0	16.833 3	16.151 8	20.458 3	6.048 7	3.000 0	29.000 0
西	1 529	中断前	20.875 0	27.000 0	27.045 8	32.187 5	8.800 9	7.000 0	53.500 0
		中断后	19.312 5	25.250 0	24.918 7	30.437 5	7.729 3	4.750 0	44.500 0
		下一间隔	20.062 5	25.500 0	25.378 5	31.187 5	7.808 8	4.000 0	48.750 0
北	751	中断前	28.875 0	33.833 3	34.374 6	39.083 3	8.559 1	20.166 7	65.333 3
		中断后	21.500 0	28.250 0	28.529 6	35.208 3	9.501 6	9.833 3	48.333 3
		下一间隔	21.750 0	28.666 7	28.998 3	35.416 7	9.723 7	11.500 0	50.333 3

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表 7 持续中断定义下交叉口各入口方向通行能力估计结果

Table 7. Estimation results of capacity for entry directions of intersection under continuous breakdown

入口方向	车道序号	I_j= (b_j-1, b_j]	N_j	d_j	$\overset{\land}{q} (j)$	$\overset{\land}{p} = 1 - \overset{\land}{q} (j)$	$\overset{\land}{Ρ} (j)$	20%估计值	20%期望估计值	估计值汇总	期望估计值汇总
东	1	(46, 50]	90	53	0.588 9	0.411 1	0.127 6	38	35	141	133
	1	(50, 54]	37	37	1.000 0	0.000 0	0.000 0	38	35
	2	(46, 50]	94	59	0.627 7	0.372 3	0.122 0	38	35
	2	(50, 54]	35	35	1.000 0	0.000 0	0.000 0	38	35
	3	(59, 64]	25	20	0.800 0	0.200 0	0.008 8	29	28
	3	(64, 69]	5	5	1.000 0	0.000 0	0.000 0	29	28
	4	(64, 71]	42	35	0.833 3	0.166 7	0.012 4	36	35
	4	(71, 78]	7	7	1.000 0	0.000 0	0.000 0	36	35
南	5	(12, 18]	8	3	0.375 0	0.625 0	0.555 6	12	11	119	112
	5	(18, 24]	5	5	1.000 0	0.000 0	0.000 0	12	11
	6	(12, 18]	7	2	0.285 7	0.714 3	0.625 0	12	11
	6	(18, 24]	5	5	1.000 0	0.000 0	0.000 0	12	11
	7	(22, 24]	83	47	0.566 3	0.433 7	0.158 6	18	17
	7	(24, 26]	36	36	1.000 0	0.000 0	0.000 0	18	17
	8	(38, 42]	97	72	0.742 3	0.257 7	0.070 2	30	29
	8	(42, 46]	25	25	1.000 0	0.000 0	0.000 0	30	29
	9	(18, 20]	21	12	0.571 4	0.428 6	0.219 5	16	14
	9	(20, 22]	9	9	1.000 0	0.000 0	0.000 0	16	14
	10	(67, 73]	1	0	0.000 0	1.000 0	0.015 9	31	30
	10	(73, 79]	1	1	1.000 0	0.000 0	0.000 0	31	30
西	11	(36, 39]	113	51	0.451 3	0.548 7	0.253 1	30	28	128	120
	11	(39, 42]	62	62	1.000 0	0.000 0	0.000 0	30	28
	12	(56, 61]	54	38	0.703 7	0.296 3	0.028 9	41	39
	12	(61, 66]	16	16	1.000 0	0.000 0	0.000 0	41	39
	13	(51, 56]	4	1	0.250 0	0.750 0	0.050 9	26	24
	13	(56, 61]	3	3	1.000 0	0.000 0	0.000 0	26	24
	14	(56, 61]	37	25	0.675 7	0.324 3	0.017 9	31	29
	14	(61, 66]	12	12	1.000 0	0.000 0	0.000 0	31	29
北	15	(36, 41]	5	2	0.400 0	0.600 0	0.176 5	26	23	216	238
	15	(41, 46]	3	3	1.000 0	0.000 0	0.000 0	26	23
	16	(65, 71]	4	1	0.250 0	0.750 0	0.600 0	33	52
	16	(71, 77]	3	3	1.000 0	0.000 0	0.000 0	33	52
	17	(36, 39]	129	78	0.604 7	0.395 3	0.203 2	33	31
	17	(39, 42]	51	51	1.000 0	0.000 0	0.000 0	33	31
	18	(86, 94]	130	94	0.723 1	0.276 9	0.151 9	78	76
	18	(94, 102]	36	36	1.000 0	0.000 0	0.000 0	78	76
	19	(36, 39]	40	26	0.650 0	0.350 0	0.0593	27	26
	19	(39, 42]	14	14	1.000 0	0.000 0	0.000 0	27	26
	20	(37, 40]	4	2	0.500 0	0.500 0	0.040 0	19	30
	20	(40, 43]	2	2	1.000 0	0.000 0	0.000 0	19	30
合计	持续中断定义下的信号交叉口5 min流量估计值/pcu									604	603
合计	持续中断定义下的信号交叉口通行能力估计值/ (pcu·h^-1)									7 248	7 236

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表 8 早晚高峰最大小时流量和高峰小时流率

Table 8. Maximum traffic flows in morning and evening peaks and peak hourly flow rates

日期	最大小时流量/ (pcu·h^-1)	高峰小时流率/ (pcu·h^-1)	日期	最大小时流量/ (pcu·h^-1)	高峰小时流率/ (pcu·h^-1)	日期	最大小时流量/ (pcu·h^-1)	高峰小时流率/ (pcu·h^-1)
9月19日	6 696	7 264	9月29日	6 666	7 104	10月9日	7 024	7 304
9月20日	6 648	6 816	9月30日	6 578	7 004	10月10日	7 038	7 492
9月21日	6 719	7 184	10月1日	6 066	6 424	10月11日	6 892	7 104
9月22日	6 606	7 028	10月2日	6 134	6 488	10月12日	6 965	7 128
9月23日	6 766	6 980	10月3日	6 412	6 652	10月13日	7 175	7 472
9月24日	6 708	6 956	10月4日	6 633	7 016	10月14日	6 797	7 108
9月25日	6 644	6 732	10月5日	6 693	6 996	10月15日	6 714	7 096
9月26日	6 820	7 292	10月6日	6 887	7 112	10月16日	6 929	7 308
9月27日	6 766	6 980	10月7日	6 672	6 852	10月17日	7 071	7 208
9月28日	6 716	6 828	10月8日	6 941	7 256

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