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协同考虑脆弱性与可靠性的城市道路网络设计

吕彪 刘一骝 刘海旭

吕彪, 刘一骝, 刘海旭. 协同考虑脆弱性与可靠性的城市道路网络设计[J]. 西南交通大学学报, 2019, 54(5): 1093-1103. doi: 10.3969/j.issn.0258-2724.20180812
引用本文: 吕彪, 刘一骝, 刘海旭. 协同考虑脆弱性与可靠性的城市道路网络设计[J]. 西南交通大学学报, 2019, 54(5): 1093-1103. doi: 10.3969/j.issn.0258-2724.20180812
LÜ Biao, LIU Yiliu, LIU Haixu. Urban Road Network Design with Balance between Vulnerability and Reliability[J]. Journal of Southwest Jiaotong University, 2019, 54(5): 1093-1103. doi: 10.3969/j.issn.0258-2724.20180812
Citation: LÜ Biao, LIU Yiliu, LIU Haixu. Urban Road Network Design with Balance between Vulnerability and Reliability[J]. Journal of Southwest Jiaotong University, 2019, 54(5): 1093-1103. doi: 10.3969/j.issn.0258-2724.20180812

协同考虑脆弱性与可靠性的城市道路网络设计

doi: 10.3969/j.issn.0258-2724.20180812
基金项目: 国家自然科学基金资助项目(51278429);教育部人文社会科学研究青年基金资助项目(18YJC630115);中央高校基本科研业务费专项资金资助(2682018CX28)
详细信息
    作者简介:

    吕彪(1980—),男,讲师,博士,研究方向为交通系统优化、智能交通系统理论与方法,E-mail:swjtu_lb@126.com

  • 中图分类号: U491

Urban Road Network Design with Balance between Vulnerability and Reliability

  • 摘要: 根据常态事件下出行者风险规避的路径选择行为和非常态事件下兼具风险规避与后悔规避的路径选择行为,分别以可靠性和脆弱性指标描述常态与非常态事件下的路网性能,构建了协同考虑脆弱性与可靠性的城市道路网络设计一主双从规划模型,其中上层模型为满足可靠性约束条件下的路网脆弱性指标最优(路网可达性最高),下层模型分别为基于效用理论和后悔理论的随机用户均衡模型. 算例结果表明:与仅考虑脆弱性的模型相比,本文提出的模型在牺牲一定可达性的基础上可获得较高的路网可靠性;当投资预算为0.9 × 107时,平均路网可达性与路网可靠性分别为0.138 8和0.969 6,而仅考虑脆弱性的模型获得的对应指标分别为0.140 5和0.334 1,可达性指标减少了1.20%,可靠性指标增加了190.21%;此外,如果忽视出行决策行为差异,可能获得偏离实际的次优,甚至错误的网络设计方案,无法实现预期设计目标.

     

  • 图 1  Nguyen and Dupuis网络

    Figure 1.  Nguyen and Dupuis network

    表  1  路段路径关联关系

    Table  1.   Link-route incidence relationship

    OD对路径编号路段序列
    (1,2) 1 2→18→11
    2 2→17→7→9→11
    3 2→17→7→10→15
    4 2→17→8→14→15
    5 1→5→7→9→11
    6 1→5→7→10→15
    7 1→5→8→14→15
    8 1→6→12→14→15
    (4,3) 9 3→5→7→10→16
    10 3→5→8→14→16
    11 3→6→12→14→16
    12 4→12→14→16
    13 4→13→19
    14 3→6→13→19
    下载: 导出CSV

    表  2  投资预算对网络设计的影响

    Table  2.   Effects of investment budgets on network design

    变量B = 0.8 × 107B = 0.9 × 107B = 1.0 × 107
    协同模型脆弱性模型协同模型脆弱性模型协同模型脆弱性模型
    x1428.5789.91110.49133.9436.8191.62
    x13249.38202.09240.55186.98243.65234.69
    x4199.78132.82274.94170.21216.42203.16
    x525.8449.273.6936.78115.8552.68
    x732.4235.674.7683.3046.29112.08
    x312.7921.2549.8744.4916.7479.79
    x164.4630.712.8070.8169.4314.15
    x1520.026.863.5068.1644.378.45
    x2152.1953.0188.6211.98104.2245.49
    x10.5737.942.475.559.548.70
    x60.0021.563.784.940.002.74
    x120.6432.0115.100.7220.5722.39
    x100.000.870.0012.970.1931.85
    x112.5329.2221.5137.3516.1319.02
    x80.0222.7613.840.962.0028.79
    x170.0415.110.000.530.007.60
    x1969.753.632.850.0033.709.29
    x90.9714.9840.6113.0323.5012.01
    x180.000.3320.6017.110.0015.11
    ψm,sysx0.134 50.135 50.138 80.140 50.141 10.141 9
    φsysx0.975 80.455 00.969 60.334 10.982 90.749 7
    下载: 导出CSV

    表  4  能力扩展路段数量对网络设计的影响

    Table  4.   Effects of number of links with capacity enhancement on network design

    变量M = 15M = 17M = 19
    协同模型脆弱性模型协同模型脆弱性模型协同模型脆弱性模型
    x14 38.25 129.36   31.54 178.38   110.49 133.94
    x13 232.03 151.98   230.48 274.24   240.55 186.98
    x4 228.77 142.18   244.87 125.60   274.94 170.21
    x5 25.28 53.17   49.53 38.48   3.69 36.78
    x7 30.01 103.18   68.60 33.43   4.76 83.30
    x3 33.76 87.67   18.09 22.36   49.87 44.49
    x16 26.53 40.40   22.30 51.48   2.80 70.81
    x15 31.24 48.12   13.57 24.69   3.50 68.16
    x2 114.29 41.33   127.52 34.83   88.62 11.98
    x1 27.24 7.72   23.48 35.19   2.47 5.55
    x6 6.46 17.33   0.42 11.71   3.78 4.94
    x12 4.70 14.75   7.26 4.21   15.10 0.72
    x10 26.77 21.45   13.15 4.63   0.00 12.97
    x11 12.56 35.02   7.79 40.15   21.51 37.35
    x8 62.03 6.00   0.72 5.39   13.84 0.96
    x17       27.10 3.09   0.00 0.53
    x19       13.11 11.71   2.85 0.00
    x9             40.61 13.03
    x18             20.60 17.11
    ψm,sysx 0.137 2 0.139 5   0.138 5 0.140 4   0.138 8 0.140 5
    φsysx 0.968 7 0.378 8   0.984 3 0.415 0   0.969 6 0.334 1
    下载: 导出CSV

    表  3  能力扩展方案差异对网络设计的影响(M = 15)

    Table  3.   Effects of differences in capacity enhancement schemes on network design (M = 15)

    基于饱和度的方案基于通行能力的方案
    变量协同模型脆弱性模型变量协同模型脆弱性模型
    x1438.25129.36x4282.12194.95
    x13232.03151.98x13255.55231.87
    x4228.77142.18x134.4180.78
    x525.2853.17x2102.8333.16
    x730.01103.18x37.0726.68
    x333.7687.67x541.2060.98
    x1626.5340.40x641.6544.10
    x1531.2448.12x734.7741.21
    x2114.2941.33x89.205.81
    x127.247.72x94.140.21
    x66.4617.33x108.620.14
    x124.7014.75x118.154.83
    x1026.7721.45x120.2117.81
    x1112.5635.02x1458.02124.37
    x862.036.00x1512.0233.06
    ψm,sysx0.137 20.139 5ψm,sysx0.139 00.140 6
    φsysx0.968 70.378 8φsysx0.970 10.607 5
    下载: 导出CSV

    表  5  参数γ的变化对网络设计的影响

    Table  5.   Effects of change in coefficient γ on network design

    γ方案1 方案2 方案3
    ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)
    0.050.134 50.975 80.138 80.969 60.141 10.982 9
    0.010.329 20.998 70.323 40.560 70.332 80.997 3
    0.020.264 00.998 00.260 70.547 80.270 10.996 5
    0.030.211 20.996 10.210 60.527 40.218 50.994 8
    0.040.168 60.990 0.169 30.497 70.175 90.991 3
    0.060.107 30.934 60.107 90.400 40.112 70.961 9
    0.070.085 40.842 90.085 60.334 90.089 70.910 8
    下载: 导出CSV

    表  8  需求波动系数变化对网络设计的影响

    Table  8.   Effects of change in demand variation coefficient on network design

    变量方案1方案2方案3
    ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)
    ρ0 = 50, ρ = 800.134 50.975 80.138 80.969 60.141 10.982 9
    ρ0 = 10, ρ = 300.135 91.000 00.140 11.000 00.142 31.000 0
    ρ0 = 20, ρ = 500.135 40.999 80.139 60.998 70.141 80.999 8
    ρ0 = 30, ρ = 700.134 80.997 00.139 10.992 90.141 30.998 1
    ρ0 = 60, ρ = 1000.134 00.958 20.138 30.954 80.140 60.969 0
    ρ0 = 80, ρ = 1200.133 40.916 00.137 80.922 10.140 10.933 0
    ρ0 = 100, ρ = 1500.132 60.871 40.136 90.887 10.139 30.892 1
    下载: 导出CSV

    表  6  参数κ的变化对网络设计的影响

    Table  6.   Effects of change in coefficient κ on network design

    κ方案1方案2方案3
    ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)
    0.050.134 50.975 80.138 80.969 60.141 10.982 9
    0.010.133 80.975 80.138 30.969 60.140 60.982 9
    0.500.138 50.975 80.142 10.969 60.144 00.982 9
    1.000.139 20.975 80.142 80.969 60.144 60.982 9
    1.500.138 80.975 80.142 40.969 60.144 30.982 9
    2.000.138 00.975 80.141 60.969 60.143 70.982 9
    2.500.137 10.975 80.140 70.969 60.142 90.982 9
    下载: 导出CSV

    表  7  参数θ的变化对网络设计的影响

    Table  7.   Effects of change in coefficient θ on network design

    θ方案1方案2方案3
    ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)ψm,sys (x)φsys (x)
    0.100.134 50.975 80.138 80.969 60.141 10.982 9
    0.010.124 80.998 50.131 20.992 80.134 20.997 0
    0.050.130 60.993 10.135 70.984 80.138 20.992 8
    0.200.138 90.896 30.142 50.920 40.144 30.940 2
    0.300.141 50.780 80.144 70.841 10.146 30.866 8
    0.400.143 20.661 00.146 10.743 60.147 60.772 8
    0.500.139 70.555 70.147 20.639 10.148 60.678 7
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-10-08
  • 录用日期:  2018-12-21
  • 修回日期:  2018-11-23
  • 网络出版日期:  2019-07-10
  • 刊出日期:  2019-10-01

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