Statistical characteristics of individual and population mobility networks of urban heavy trucks
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摘要: 重型卡车是城市货运系统的重要组成部分，研究城市重型卡车出行网络特征，对于城市货运系统规划和管理具有潜在的参考价值．本文对中国4个典型城市的重型卡车出行网络进行统计特征分析．使用从重型卡车GPS轨迹数据中提取的出行链数据，建立了重型卡车个体出行网络，进而合并为群体出行网络．在重型卡车个体出行网络方面，发现网络连边组成的出行模体具有明显的异质性特征，节点返回步长近似服从截尾幂律分布，点权近似服从齐普夫定律，网络节点数量具有亚线性增长特征；在重型卡车群体出行网络方面，发现点权近似服从幂律尾分布，边权近似服从幂律分布，出行距离近似服从指数分布，边权与点权、距离之间的关系近似服从社会引力定律．对这些统计特征的形成机制进行了分析，并对再现这些统计特征的理论模型研究、个体群体出行网络时变特征分析、货运系统多层相依复杂网络构建等问题进行了初步探讨．Abstract: Urban heavy trucks are an important part of urban freight transportation system． The study of urban heavy trucks mobility network characteristics is of potential reference value for urban freight transportation system planning and management． Statistical characteristics of heavy trucks mobility networks in four typical cities in China are analyzed in this paper． Using the trip chains extracted from the heavy trucks GPS track data, individual heavy trucks mobility networks are established and then merged into population mobility network． It is found that in individual mobility networks, travel motif composed of connected edges of individual mobility networks has obvious heterogeneity characteristics, the node return steps approximately obey truncated power-law distribution, the node weights approximately obey Zipf’s law, the number of network nodes has sublinear growth characteristics． It is found that in population mobility networks of heavy trucks, node weights approximately obey power-law tail distribution, edge weights approximately obey power-law distribution, mobility distances approximately obey exponential distribution, relationship between edge weights, node weights and distances approximately obeys social gravity law． The underlying mechanisms of these statistical characteristics are analyzed． Theoretical model of reproducing these statistical characteristics, time-varying characteristics analysis of individual and population mobility networks, construction of multi-layer interdependent complex networks of freight systems, etc． are preliminarily discussed．
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Key words:
- urban freight /
- heavy trucks /
- mobility network /
- complex network /
- statistical characteristics
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图 1 重型卡车个体与群体出行网络构建示意
a、c. 某辆重型卡车在3 d内的出行链构成的个体出行有向时序网络；b. 上下2辆重型卡车出行链合并后构成的群体出行无向加权网络．图中圆点面积表示节点权值，直线宽度表示连边权值．
图 2 北京市重型卡车群体出行网络地图
图中圆点表示群体出行网络节点，圆点面积与点权成正比；直线表示网络连边，线宽与边权成正比，颜色深浅与边权相关．为更清晰地展示北京市的重型卡车群体出行空间分布，该图只绘制了边权>20的连边及其两端节点．
图 3 城市重型卡车个体出行网络连边统计特征
a~d. 重型卡车个体出行网络连边数量分布$p(l)$，其中l表示每个个体出行网络中包含的连边数量，p(l)表示连边数量为l的个体出行网络数量在城市个体出行网络总数量中所占的比例；e~h. 重型卡车出行模体（motif）统计结果；i~l. 重型卡车个体出行网络节点返回步长分布$p(\tau)$，表示返回步长为τ的出行返回数量在城市个体出行网络出行返回总数量中所占的比例．
图 4 城市重型卡车个体出行网络节点统计特征
a~d. 重型卡车个体出行网络节点数量分布$p(n)$，其中n表示每个个体出行网络包含的节点数量，p(n)表示节点数量为n的个体出行网络数量在城市个体出行网络总数量中所占的比例；e~h. 重型卡车个体出行网络节点访问频率分布，其中$k$为节点度（即被访问次数）的排序，$f_k$为度排序第$k$的节点被访问的频率，圆形、正方形、三角形符号分别表示节点数量为10、20和30的个体出行网络节点被访问频率；i~l. 重型卡车个体出行网络节点数量$n$随时序$t$的增长关系．
图 5 城市重型卡车群体出行网络统计特征
a~d. 重型卡车群体出行网络点权分布$p(s)$，其中s表示群体出行网络节点的权值，p(s)表示点权为s的节点数量在城市重型卡车群体出行网络节点总数量中所占的比例；e~h. 重型卡车群体出行网络边权分布$p(w)$，其中w表示群体出行网络连边的权值，p(w)表示边权为w的连边数量在城市重型卡车群体出行网络连边总数量中所占的比例；i~l. 重型卡车群体出行距离分布$p(d)$，其中d表示重型卡车群体出行网络连边的长度，p(d)表示长度为d的连边上的出行量在城市重型卡车出行总量中所占的比例；m~p. 节点$i$、$j$间距离$d_{ij}$与节点i、j间边权比点权$w_{ij}/s_i s_j$的对数关系．
表 1 中国典型城市重型卡车个体群体出行网络基本统计数据
城市 重型卡车数量 个体出行网络边总数 点总数 群体出行网络节点数 连边数 总边权 出行总距离/km 北京 18510 650757 261997 15983 249107 588718 10151063 天津 23943 774654 379312 10697 290692 699659 13925336 重庆 34667 988170 455400 10631 276076 725205 15182454 上海 41608 1332216 632930 16096 497232 1184977 21708582 
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