Characteristics and vulnerability of rail transit network besed on perspective of passenger flow characteristics
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摘要: 为提高城市轨道交通网络脆弱性评估的客观性, 将乘客需求特性集成到网络脆弱性的计算中; 在城市轨道交通网络Space L空间下静态拓扑结构的基础上, 以客流为权重建立了轨道交通加权网络; 基于客流指标提出了车站连接强度和加权节点介数, 用于反映动态网络结构特征, 度量节点间相互作用强度; 针对城市轨道交通网络客流的时空特性, 结合网络客流需求特性, 基于出行消耗最大容限阈值, 构建了站点故障条件下的乘客有效路径子图和网络客流的OD损失率, 进而评估城市轨道交通网络的脆弱性; 以西安城市轨道交通网络为例, 从网络客流视角分析了城市轨道交通网络特征及其脆弱性。研究结果表明: 西安市轨道交通网络具有小世界网络特性, 平均路径长度为10.7, 其中小寨站和北大街站为网络关键节点, 其车站连接强度分别为166 795、149 059, 加权节点介数分别为0.365、0.369, 这两个站点的中断对西安市轨道交通网络效率的影响分别为40.1%、39.4%;乘客出行容限阈值极大地影响着网络中站点的重要性排序, 网络脆弱性随着乘客出行容限阈值的增大而逐渐降低; 脆弱性与介数的相关性强于脆弱性与度和强度的相关性, 随着出行容限阈值的增大, 加权介数与其脆弱性的关联性逐渐降低。可见, 提出的计算指标和方法突出了客流特征与乘客需求对轨道交通网络脆弱性的影响, 能够很好地体现轨道交通网络的功能特性。Abstract: In order to improve the objectivity of vulnerability assessment of urban rail transit network, passenger demand characteristics were integrated into the calculation of network vulnerability. Based on the static topological structure of urban rail transit network established by using the Space L method, the weighted network of rail transit was established with passenger flow as the weight. Based on the passenger flow index, the station connection strength and weighted node betweenness were proposed to reflect the dynamic network structure characteristics and measure the interaction strength between nodes. Aiming at the spatial-temporal characteristics of passenger flow in urban rail transit network, combined with the demand characteristics of network passenger flow, the passenger effective path subgraph and OD loss rate of network passenger flow under the condition of station failure were defined by using the maximum travel consumption tolerance threshold to evaluate the vulnerability of urban rail transit network. Taking Xi'an urban rail transit network as an example, the features and vulnerability of urban rail transit network were interpreted from the perspective of passenger flow characteristics. Research result shows that the current rail transit network in Xi'an has the characteristic of small world network and its average path length is 10.7. Xiaozhai Station and Beidajie Station are the key nodes of the network, their connection strengths are 166 795 and 149 059, respectively, and their weighted node betweennesses are 0.365 and 0.369, respectively. The interruption of the two stations will result in 40.1% and 39.4% reduction in network efficiency. The passenger travel tolerance threshold greatly affects the importance ranking of the stations in the network. With the increase of passenger travel tolerance threshold, the network vulnerability gradually decreases. The correlation between vulnerability and betweenness is stronger than those with degree and intensity. With the increase of travel tolerance threshold, the correlation between weighted betweenness and vulnerability gradually decreases. Therefore, the calculation indicators and methods proposed in this paper highlight the impact of passenger flow characteristics and passenger demand on the vulnerability of rail transit network, which can well reflect the functional characteristics of rail transit network.
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Key words:
- urban rail transit /
- topology /
- Space L method /
- passenger flow characteristics /
- passenger demand /
- vulnerability
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图 3 西安市轨道交通高峰小时客流量分布
Figure 3. Peak hour passenger flow distribution in Xi'an rail transit
表 1 西安市轨道交通网络特征指标与取值
Table 1. Characteristic indexes and values of Xi'an rail transit network
特征指标 取值 节点数 88 边数 90 平均度 2.05 平均介数 0.11 网络直径 27 平均路径长度 10.7 平均聚类系数 0 
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表 2 指标排名前十的车站
Table 2. Top ten stations based on indexes
站点编号 D′i 站点编号 B′i 33 166 795 10 0.369 10 149 059 33 0.365 46 104 232 28 0.225 14 102 959 14 0.219 11 95 552 29 0.206 45 89 909 30 0.204 29 85 849 46 0.204 28 85 506 31 0.196 30 82 854 27 0.194 31 80 615 32 0.193
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表 3 站点脆弱性与各指标的Pearson相关系数
Table 3. Pearson correlation coefficients between vulnerabilities and indicators of stations
计算情形 指标 Di Bi D′i B′i 客流非均匀分布(实际情形) S(1.0) 0.59 0.75 0.97 0.99 S(1.5) 0.61 0.60 0.85 0.82 S(2.0) 0.56 0.47 0.76 0.72 S(2.5) 0.53 0.42 0.71 0.68 S(3.0) 0.50 0.39 0.69 0.65 客流均匀分布(假设情形) S(1.0) 0.73 0.98 0.74 0.76 S(1.5) 0.68 0.70 0.46 0.44 S(2.0) 0.60 0.56 0.36 0.35 S(2.5) 0.57 0.52 0.33 0.33 S(3.0) 0.55 0.50 0.31 0.31
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表 4 各站点脆弱性对比
Table 4. Comparison of vulnerabilities among stations
R=1 R=2 站点排名变化 站点编号 站点名称 实际OD客流分布下网络平均损失率 OD客流均匀分布下网络平均损失率 站点编号 站点名称 实际OD客流分布下网络平均损失率 OD客流均匀分布下网络平均损失率 33 小寨站 0.401 0.283 33 小寨站 0.397 0.271 0 10 北大街站 0.394 0.449 10 北大街站 0.248 0.236 0 28 安远门 0.248 0.260 14 通化门 0.233 0.351 1 14 通化门 0.245 0.378 45 吉祥村 0.220 0.130 3 27 龙首原 0.240 0.245 44 太白南路 0.202 0.109 5 46 大雁塔 0.222 0.315 34 纬一街 0.188 0.130 9 45 吉祥村 0.220 0.130 35 会展中心 0.176 0.109 10 29 钟楼 0.214 0.145 43 科技路 0.171 0.089 10 26 大明宫西 0.210 0.230 9 洒金桥 0.140 0.188 15 44 太白南路 0.202 0.109 23 行政中心 0.139 0.193 12
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