考虑道路收费的系统最优高速公路改扩建交通分流方法

田龙; 郭月利; 袁雪强; 方地久; 曾强

doi:10.3963/j.jssn.1674-4861.2024.03.009

考虑道路收费的系统最优高速公路改扩建交通分流方法

doi: 10.3963/j.jssn.1674-4861.2024.03.009

田龙^1,,
郭月利²,
袁雪强³,
方地久³,
曾强^4, ,

1.
深圳市深汕港口运营有限公司广东深圳 518000
2.
广东省交通规划设计研究院集团股份有限公司广州 510000
3.
深圳惠盐高速公路有限公司广东深圳 518000
4.
华南理工大学土木与交通学院广州 510000

基金项目:

国家自然科学基金项目 52172345

详细信息

作者简介:
田龙(1982—)，高级工程师. 研究方向：公路与港口运营管理. E-mail: 350962118@qq.com

通讯作者:
曾强(1988—)，博士，副教授. 研究方向：道路交通安全、公共交通运营与管理. E-mail: zengqiang@scut.edu.cn

中图分类号: U491.5+4
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-18
- 网络出版日期: 2024-10-21

A System Optimization Model of Traffic Divergence for Freeway Reconstruction and Expansion Considering Road Charge

1.
Shenzhen Shenshan Port Operation Company Limited, Shenzhen 518000, China
2.
Guangdong Communication Planning & Design Institute Group Company Limited, Guangzhou 510000, China
3.
Shenzhen Huiyan Expressway Company Limited, Shenzhen 518000, China
4.
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510000, China

摘要

摘要: 交通分流是保障高速公路改扩建期间交通运行效率的重要措施。然而，目前国内高速公路改扩建工程多依靠管理人员经验性地确定分流措施，缺乏系统客观的分流方法，分流效果有待进一步提升。根据区域分流路网的道路特征，在行程时间基础上考虑道路收费对出行者路径选择的影响，构建路段阻抗函数。从交通管理者角度出发，以路网总出行阻抗最小为优化目标，考虑需求守恒、路径路段流量关系和路径流量非负约束，建立系统最优高速公路改扩建交通分流模型。分析模型的卡罗需-库恩-塔克(Karush-Kuhn-Tucker，KKT) 条件，设计基于梯度投影的路径型算法，求解得到路网各起讫点(origin-destination，OD)之间的分流路径和路径流量。以广东省某高速公路改扩建工程为例，量化分析不分流、分流时不考虑道路收费和分流时考虑道路收费3种情形下的整体路网及改扩建高速施工路段交通运行状况。结果表明：分流时不考虑道路收费，改扩建高速施工路段交通量平均降低27.72%，饱和度降低0.09，平均车速提高4.26 km/h；分流时考虑道路收费后，改扩建高速施工路段交通量平均降低44.8%，饱和度降低0.4，平均车速提高12.98 km/h，道路通行效率得到有效改善，同时分流并未导致路网中其它路段交通运行情况变差。以上结论验证了本文所提出的改扩建交通分流方法的有效性和优越性。
- 交通工程 /
- 高速公路 /
- 交通分流 /
- 系统最优 /
- 道路收费
Abstract: Traffic divergence is an important measure to ensure the efficiency of traffic operation during the reconstruction and expansion of freeways. However, currently the expressway reconstruction and expansion projects in China mainly rely on the managers to determine the divergence measures empirically, of which the performance needs to be further improved. Meanwhile, there is lack of systematic and objective divergence methods. According to the road characteristics of regional divergence network, a road impedance function is developed by combining the impact of road toll on travelers' route choice with travel time. From the perspective of traffic managers, taking the minimum travel impedance of the road network as the optimization objective, the system optimization model of traffic divergence for reconstruction and expansion of freeway is established considering the balance of demand and supply, the relationship between path and link flows and the non-negative constraint of route flow. The Karush-Kuhn-Tucker (KKT) conditions of the model is analyzed, and an algorithm based on gradient projection is designed to obtain the divergence path and path flow among origin-destination (OD) pairs in the road network. Taking a reconstruction and expansion project of freeway in Guangdong Province as an example, the traffic operation states of the entire road network and the construction section are modeled under three conditions of no divergence, divergence without road toll and divergence with road toll. The results show that: ①Without considering the road toll, the average traffic volume of the section of reconstruction and expansion decreases by 27.72%, the saturation decreases by 0.09, and the average speed increases by 4.26 km/h. ② Taking road toll into consideration during the diversion, the traffic volume of the section of reconstruction and expansion is reduced by 44.8% on average, the saturation is reduced by 0.4, and the average speed is increased by 12.98 km/h. The road traffic efficiency is effectively improved, and the divergence does not cause deterioration of the traffic operation of other sections in the road network. Such conclusions confirm the effectiveness and superiority of the traffic divergence method proposed in this paper.
- traffic engineering /
- freeway /
- traffic divergence /
- system optimization /
- road toll

HTML全文

图 1 梯度投影算法流程图

Figure 1. Flow chart of gradient projection algorithm

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图 2 分流路网拓扑图

Figure 2. Topology of diversion road network

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图 3 改扩建前路网交通参数

Figure 3. Traffic parameters of road network before reconstruction and expansion

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图 4 改扩建中不分流时项目路交通参数

Figure 4. Project road traffic parameters without diversion during reconstruction and expansion

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图 5 不考虑道路收费分流的路网交通参数

Figure 5. Traffic parameters of road network without road charge

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图 6 改扩建高速不考虑道路收费分流后交通参数

Figure 6. Traffic parameters of expanded expressway when implementing traffic divergence without road charge

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图 7 收敛曲线

Figure 7. Convergence curve

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图 8 考虑道路收费分流的路网交通参数

Figure 8. Traffic parameters of road network with road charge

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图 9 改扩建高速考虑道路收费分流后交通参数

Figure 9. Traffic parameters of expanded expressway when implementing traffic divergence with road charge

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图 10 不同场景路段交通参数对比

Figure 10. Comparison of traffic parameters in different scenarios and sections

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表 1 路段相关参数

Table 1. Parameters of link

路段编号	自由流时间/h	通行能力/(pcu/d)	长度/km	收费率/(元/h)
1，4	0.015 125	68 856	1.21	0.45
2，13	0.01	198 000	0.8	-
3，18	0.01	198 000	0.8	-
5，8	0.039 15	68 856	3.132	0.45
6，34	0.001 5	158 400	0.1	-
7，36	0.025	211 200	3	0.45
9，11	0.095 4	68 856	7.63	0.45
10，52	0.035	211 200	4.2	0.45
12，55	0.003 7	163 200	0.25	-
14，16	0.019 6	198 000	1.4	-
15，22	0.015 6	118 800	1	-
17，26	0.012 8	244 800	1	-
19，20	0.001 72	79 200	0.1	-
21，29	0.017 2	79 200	1	-
23，27	0.018 7	118 800	1.2	-
24，30	0.023 4	118 800	1.5	-
25，32	0.018 7	118 800	1.2	-
28，39	0.012 8	244 800	1	-
31，35	0.010 9	118 800	0.7	-
33，40	0.017 2	79 200	1	-
37，41	0.020 6	79 200	1.2	-
38，43	0.122 5	211 200	14.7	0.45
42，45	0.042 2	244 800	3.3	-
44，50	0.034	151 200	3.4	0.6
46，48	0.010 3	158 400	0.7	-
47，56	0.063 9	285 600	5	-
49，53	0.081 2	158 400	5.5	-
51，59	0.128	151 200	12.8	0.6
54，61	0.014 8	158 400	1	-
57，60	0.227 3	163 200	15.4	-
58，63	0.075 3	163 200	5.1	-
62，64	0.110 1	79 200	6.4	-
注：“-”表示该路段不收费。

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表 2 区域内出行OD交通量矩阵

Table 2. The OD traffic volume matrix of intra-regional travel 单位: pcu/d

起点	终点
起点	1	2	3	4	5	8	22	24
1	0	38 353	27 699	21 910	26 439	11 480	17 857	25 298
2	35 763	0	12 096	6 055	7 994	3 381	3 682	7 931
3	34 972 12	383	0	7 840	4 571	1 876	2 324	5 180
4	21 623	20 111	10 661	0	26 852	7 707	6 237	13 412
5	25 886	7 602	5 180	25 662	0	2 135	3 143	15 239
8	10 899	3 206	1 918	7 441	2 898	0	1 078	13 790
22	20 391	3 584	2 765	6 671	3 829	1 932	0	63 742
24	25 795	6 727	5 313	13 300	13 909	13 867	56 721	0

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表 3 参数设置

Table 3. Parameter setting

参数	取值
α	0.15
β	4
ε	0.001
N	200

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表 4 分流路径信息

Table 4. Path information of traffic divergence

OD	路径编号	路段序列	路径流量(/pcu/d)
(1，2)	1	3-19-21-31-34	2 471.623 075
(1，2)	2	1	35 881.376 92
(1，3)	1	3-19-21-31-34-1	1 558.150 357
(1，3)	2	1-5	26 140.849 64
(1，4)	1	2-15-23-28-42-47-55	3 788.595 379
(1，4)	2	2-14-17-28-42-47-55	18 121.404 62
(2，1)	1	4	31 454.158 28
(2，1)	2	6-35-29-20-18	4 308.841 723
(2，3)	-	5	12 096
(2，4)	-	6-35-30-23-28-42-47-55	6 055
(3，1)	1	8-4	32 651.746 49
(3，1)	2	8-6-35-29-20-18	2 320.253 513
(3，2)	-	8	12 383
(3，4)	-	9	7 840
(4，1)	1	12-56-45-39-26-16-13	18 048.263 24
(4，1)	2	12-56-45-39-27-22-13	3 574.736 763
(4，2)	-	12-56-45-39-27-24-31-34	20 111
(4，3)	-	11	10 661

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