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摘要: 为了定量描述中国公路货运枢纽体系结构现状, 将公路货运量作为货运枢纽的规模参数, 推导了分维数的计算公式, 选取1997~2007年的货运量统计数据, 计算了200个公路货运枢纽规模分布的分维数。数据拟合发现: 1997~1999年公路货运枢纽的规模分布具有双分形特征, 2000~2007年的规模分布呈单分形结构, 且分维数介于1.464 6~1.570 1间, 公路货运枢纽体系的规模分布与城镇体系基本一致。分析结果表明: 中国公路货运枢纽体系规模分布从双分形到单分形的演化显示其发育较好, 需加强大型公路货运枢纽建设, 以进一步优化公路货运枢纽体系结构。Abstract: In order to quantitatively evaluate the system topology of Chinese truck transportation hubs in recent years, highway freight volume was regarded as a size index of truck transportation hub.A novel formula for exactly calculating the fractal dimension of size-distribution of the truck transportation hub was presented.The fractal dimensions of size-distributions of 200 largest truck transportation hubs during 1997~2007 were calculated by the formula based on the statistical data of highway freight volumes.Computation result shows that the size-distributions of truck transportation hubs during 1997~1999 are bi-fractal, while that are single fractal and the fractal dimensions are between 1.464 6 and 1.570 1 during 2000~2007, and the size-distribution of truck transportation hub system is adapted to city system.The evolvement of the fractal topology from bi-fractal to single fractal indicates a rational evolutionary progress of size-distributions of truck transportation hubs, and large truck transportation hubs should be supported to optimize the structure of truck transportation hub system.
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图 3 1997~2007年城市规模分布拟合曲线
Figure 3. Size-distribution fitting curves of cities during 2000~2007
表 1 枢纽体系规模分布参数
Table 1. Size-distribution parameters of hub system
参数 年份 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 D1 1.712 6 1.688 2 1.761 3 R12 0.992 3 0.986 9 0.988 8 D2 0.488 7 0.598 8 0.639 4 R22 0.955 8 0.975 8 0.978 7 D 1.464 6 1.503 3 1.524 5 1.525 6 1.469 3 1.570 1 1.566 7 1.503 8 R2 0.965 9 0.973 1 0.970 0 0.970 4 0.969 9 0.964 7 0.978 1 0.969 5 
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表 2 城镇体系规模分布参数
Table 2. Size-distribution parameters of city system
参数 年份 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 q 0.586 6 0.660 9 0.656 7 0.625 0 0.630 4 0.637 0 0.637 3 0.633 1 0.646 4 0.637 5 0.635 8 R2 0.961 4 0.969 0 0.973 1 0.976 5 0.982 1 0.984 7 0.986 7 0.986 8 0.988 0 0.987 5 0.987 2 D 1.638 9 1.466 2 1.481 8 1.562 4 1.557 9 1.545 8 1.548 3 1.558 7 1.528 5 1.549 0 1.552 7
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