城市轨道交通站点换乘供需分形量化研究

Fractal Quantization of Supply and Demand of Urban Rail Transit Stations

城市轨道交通线网在规划时,总是谋求客运供给能力与换乘需求之间的平衡(一致性),而线网布局的供需一致性可以通过站点布局的供需一致性表示。基于分形理论,针对轨道交通线网站点的分布形态(客运供给能力)和站点的换乘需求(需求),提出了站点分布-半径维数、站点换乘需求-半径维数。为量化站点的换乘供需在空间分布上的一致性(供需平衡),提出了分形一致性指数。最后以北京市轨道交通线网为例,验证了模型和算法的有效性,并对算法中涉及的出行需求(OD矩阵)进行了敏感性分析,讨论了出行行为对于分形维数和一致性指数产生的影响。结果显示分形维数、一致性指数能够较好地描述轨道交通线网的供需平衡特征。

In the metropolitan traffic planning, it is always considered to keep the balance （consistency） between passenger transport capacity and transfer demand, and the consistency of network layout can be represented by the consistency of station layout. According to the fractal theory, the station distribution-radius fractal dimension which represents the distribution form （ supply capacity of passenger transport） of rail transit stations and the station transfer demand-radius fraetal dimension which represents the transfer demand （demand） of rail transit stations are provided. In order to quantify the consistency of spatial distribution of station transfer for rail transit stations （the balance of supply capacity and demand ） , a consistency index based on fractal dimension is proposed. Taking the rail transit network of Beijing for example, the validation of the model and algorithm are verified, and the sensitivity analysis on travel demand from the algorithm （ OD matrix） is conducted, the impact of travel behavior on the fractal dimension and the consistency index is discussed. The result shows that the fractal dimension and the consistency index can be used for the description on the balance of supply and demand for stations of rail transit network.