地铁改革——中文版.doc

Introduction.With the continuous expansion of a city, the subway network plays a more and more important role as means of transportation, especially in large metropolises. As a result, more and more research is being done on the study of urban transit railway systems.随着城市的不断扩张，地铁作为一种运输手段，起着越来越重要的作用，特别是在大型城市。因此，有越来越多关于城市铁路运输系统的研究。Many of those studies are in the domain of complex networks 17, especially in the first decade of this century,after two milestones: the small-world network 8 and the scale-free network 9. Most of the research studies on these physical networks focus on static analysis and comparisons among different subway networks. 许多这些研究都是在复杂网络 1-7 的领域，尤其是在本世纪的第一个十年里，在两个里程碑之后：小世界网络 8和无标度网络 9 。大多数这些物理网络的调查研究侧重于在对不同的地铁网络的静态分析和比较。However,networks are dynamic and will change along with the development of the city or the new plan of the city.Thus,the static analysis could not reflect comprehensively the characteristics of a network. More specifically, different from other complex networks, such as air transportation net-works 10, social networks 11 and the Internet 12, subway networks are two-dimension networks and are strongly related to a citys layout, which means that the evolution of subway networks is of special traits 13. 然而，网络是动态的，会随着城市的发展或新计划的制定而改变。因此，静态分析不能反映网络的全面的特性。更具体地，与其他复杂的网络，诸如航空运输网络中 10 ，社会网络11和因特网12不同，地铁网络是两维网络，并且与一个城市的布局密切相关，这意味着该地铁网络的演进具有特殊性 13 。Moreover, the growth process determines partly topological characteristics of networks14and further interacts with the facilities on the ground15,16and human mobility patterns17,18.此外，生长过程部分决定了网络的类型特性 14 ，并与地面上的设施15,16和人类移动模式17,18相互作用。In brief, the infrastructure of subway networks, a fundamental element, should be studied firstly and understood comprehensively within a time period. Although the evolution of networks has already been studied, such as the scale-free developing model with two conditions 19 and the micro dynamic model of worlds air transportation net-work 20, the evolution of subway networks has rarely been studied beyond a descriptive model 21. The existing model does not appropriately fit subway networks and assumes that they have the same mode at every step,which may not be true.总之，作为一个根本的要素，应首先研究地铁网络的基础设施，并且在一个时间周期内全面理解。虽然已经对网络的演进进行了研究，如，两个条件的无标度发展模式19和全球航空运输网络 20 的微观动态模型的，但很少有通过描述性模型来研究地铁网络的演进 21 。现有的模型不能恰当地符合地铁网络，并假设它们每一步都具有相同的模式，这种假设可能不是真的。Meanwhile, the definition of a network is a crucial factor, since different definitions will lead to very different results even the indicators are the same 1. The previous studies of subway networks mainly focus on the role of stations and ignore the role of lines. However, for subways, the concept of lines is more important than that of stations because of the high speed of subways and the inconvenience of transfer. Therefore, a new perspective of analysis is required in which the concept of line will be involved and the characteristics of transfer could be revealed.同时，对网络的定义是一个关键的因素。即使这些指标是相同的，不同的定义也将导致非常不同的结果1。对地铁网络以前进行的研究主要集中在车站，而忽略线路。然而，因为地铁的高速传输和转移的不便，对于地铁而言，对线路的研究比对车站的研究更重要。因此，需要一个新的分析视角，将线的概念和转移的特性纳入研究范围。In this paper,we first study the Beijing Subway Network (BSN) as well as simplified evolution cases and propose a new developing model with two modes. Then, we analyze the Beijing Subway Transfer Network (BSTN) with emphasis on lines and transfer.在本文中，我们首先研究了北京地铁网络（BSN）和简化的演变情况，并通过有两种模型提出一种新的发展模式。然后，我们分析了北京地铁传输网络（BSTN），着重分析了线路和传输。Basic statistics. BSN was open to the public in 1981 and rapidly developed from 2007 to 2013, coinciding with the rising demand of new urban transport means due to an increasing burden of transport on the ground 22,23.基本统计数据- 北京地铁网络于1981年向公众开放，并于2007至2013年迅速发展，由于地面运输的负担日益加重，这与新城市交通不断增长的需求是22,23相吻合的。Figure 1 provides a general view of the development of BSN. The data of BSN is from the Beijing Metro Network Control Center and the Beijing Transportation Information Center. The new line opened in July 2013 is not included. In table 1, the development of BSN can be clearly seen. In the last seven years, the number of lines has quadrupled. The number of stations have tripled while the number of transfer stations (TStation) have sextupled, which may be an indicator for the intensification of connection.图1提供了北京地铁网络发展的一个基本介绍。北京地铁网络的数据来自北京地铁网络控制中心和北京市交通信息中心。2013年7月开设新的生产线不包括在内。在表1中，可以清楚地看到北京地铁网络的发展。在过去的七年中，线路的数量翻了两番。站台的数量增加了两倍，而转运站（TStation）的数量变成了之前的6倍，这可能是连接强化的一个指标。Degree. One of the most apparent characteristics of a network is the degree of the node in the network, regardless of the distribution or the average value. The average degree (AD) of subway networks is slightly larger than 2 3, in that most stations are not transfer stations. The AD of BSN remains on a stable level 2.06, 2.22, which belongs to 2, 2.45, the interval of AD of 30 Urban Rail Transit Networks (URTNs) 3, and 2.18, 2.73 in 24.程度。一个的网络的最明显的特征是网络中的节点的度，无论分配或平均值。地铁网络的平均度（AD）是略大于23，在大多数车站没有中转站。北京地铁网络的平均度维持在一个稳定的水平2.06，2.22，属于并且在2，2.45，30城市轨道交通网络平均度。The value of AD also reveals that the number of stations and the number of edges are in the same order, which is demonstrated in fig. 2. Actually, from the first year to the last, the two numbers are evidently close to each other.The largest difference appears in 2013, when the number of edges is 10% larger than that of stations.Meanwhile, the range of the degree (DR) is narrow, which might be a result of the consideration of the financial cost as well as the time cost of passengers. As shown in table 1, the biggest DR of BSN is 1, 5. 图2表明，平均度的值显示，站台的数量和边的数目是按照相同的顺序。事实上，从第一年到最后一年，两个数字是明显接近另一个.最大的差异出现在2013年，边的数目比站台的数量多10。同时，程度的范围是狭窄的，这可能是出于考虑财务的成本以及乘客的时间成本所致。如表1所示，北京地铁网络的最大程度范围为1,5。In this way, if the distribution is required, it will be given based on a fitting of only five points. From the perspective of statistics, this fitting is far from being meaningful.Average shortest path length. The shortest path length (SPL) measures the distance between a pair of nodes and therefore could also be seen as a representation of the transmission efficiency: the shorter the SPL between two nodes the faster the transmission between the two nodes. 以这种方式，如果需要分布，这将仅是基于5点。从统计的角度看，该嵌合并没有有意义.平均最短路径长度。最短路径长度（SPL）测量一对节点之间的距离，因此也可以被看作是传输效率的一种表示：在两个节点路径长度更短，传输更快。Therefore, the complete graph has the smallest average shortest path length(ASPL),which is 1. However,subway networks whose AD is very low are too sparse that could not be compared with the complete graph. Further-more, since the number of station and the number of edge are in the same order, the more extended the subway net-work is, the further it is away from the complete network and the longer the ASPL it has. 因此，正如1中显示的，完整的图形具有最小的平均最短路径长度（ASPL）。然而，地铁网络的平均度是非常低的，导致与完整的图形相比过于稀疏。进一步，由于站台的数目和边的数目是按照相同的顺序，地铁网络越延伸，越进一步远离完整的网络，平均最短路径长度越长。Actually, the expanded subway network is considered as better than the smaller one, in that coverage is one of the most important aspects of performance evaluations of subway networks. From another point of view, the development of subway networks will certainly not increase the SPL between existing pairs of nodes and the augmentation of the ASPL is due to the new added nodes, which might be at the very extremities of networks.其实，扩张的地铁网络被认为是比小的地铁网络更好，这是地铁网络的性能评估中最重要的方面之一。从另一个角度来看，由于新增加的可能是在网络的最末端节点，地铁网络的发展肯定不会增加在现有节点之间的最短路径长度和增强平均最短路径长度。This phenomenon is well explained in table 1 and fig. 2:with the development of BSN, its ASPL increased generally. Numerically, the ASPL of BSN started from a very low value from the perspective of subway networks and reached a high value in 2013. The statistics in 3 gives a global view of 30 subway networksASPL. Only three networks ASPL are smaller than 10 and only Seouls is larger than 16. The authors of ref. 24 also summarized that the ASPL of subway networks is almost of order 10.这种现象通过表1和图2可以得到很好的解释。随着北京地铁网络的发展，它的平均最短路径长度普遍增加。在数值上，北京地铁网络的平均最短路径长度从一个非常低的值开始增长，并于2013年达到一个高值。3中的统计数字给出了30个地铁网络的平均最短路径长度的全局视图。只有三个网络的平均最短路径长度小于10，仅首尔的大于16。参考文献24的作者还总结了地铁网络的平均最短路径长度几乎都为10。Along with the development of BSN, its ASPL values are always closed to the value of the majority of worlds sub-way networks.In addition, although the value is always in the statistic interval.the relationship between ASPL and () are different with cross-sectional data and with time series data.The former data supports that ASPL of subway networks Scales like N 1/2 24, whereas the real time series data from BSN, especially in the first four years, contradicts it. The sudden augmentation in 2013 resulted from involving Line 9 and Line Fang shan which were isolated in 2012.与世界上大多数的地铁网络的值相比，随着北京地铁网络的发展，其平均最短路径长度值总是封闭的.另外，尽管该值始终在统计，平均最短路径长度和（）之间的关系是与横截面数据和时间序列数据不同的。前面的数据支持地铁网络的平均最短路径长度，如N1/2 24，真正的时间序列数据来自北京地铁网络，尤其前四年的数据是互相冲突的。突然的增强是因为2013年的9号线和2012年方山线的分离。Clustering coefficient. Clustering coefficient (CC)is another basic but important metric. It measures the intensity of connection around one node in the network. Different from the ASPL, CC provides more local information. A node i with higher CC has better location and is more convenient to run back and forth between with other nodes. The CC of a network is the of all nodes in the network. Higher average of the CC i CC indicates a higher intensity of the local connection.聚类系数。聚类系数（CC）是另一种基本而重要的指标。它可以测量网络中的一个节点的连接的强度。与平均最短路径长度不同，聚类系数提供更多的本地信息。一个有更高聚类系数的节点有更好的位置，并在其它节点上运行来回更方便。网络的聚类系数是在网络中的所有节点。较高的平均聚类系数显示本地连接的强度更高。However, according to the definition, in order to guarantee being non zero, the node and two of its adjacent nodes have to constitute a triangle. Furthermore, the CC of a network is non zero only if the network has at least one triangle constituted by three adjacent nodes.Unfortunately, in subway networks, the group of three stations connected pairwise rarely appears. 然而，根据该定义，以保证为非零，该节点和它的两个相邻节点必须构成一个三角形。此外，只有当网络至少有三个相邻节点时，网络的聚类系数是非零。不幸的是，在地铁网络中，三站两两相连很少出现。One of the service attributes of a subway, indifferent to taking two or three more stations for transferring, leads to a relatively loose network and few adjacent triads. For this reason,the CC of subway networks is usually null, especially in early regime. As many other subway networks, 12 among30 in 3, the CC of BSN remains zero during the seven years (see table 1).地铁的服务属性，与在两个或三个以上的站之间传送的服务属性不同，导致了相对宽松的网络和几乎没有的相邻triads。出于这个原因，地铁网络的聚类系数通常为空，尤其是在早期。正如许多其他的地铁网络，30个地铁网络中的12个3，北京地铁网络的聚类系数七年保持为0（见表1）。Growth model. As costly and huge networks, subway networks are always accomplished in a relatively long period. Therefore, evaluating them from the dynamic perspective is important. Among those existing models, each model has one developing mode, although the change of nodes or edges might be different from one step to another,and the mechanism does not change 19,20. 增长模式。 - 在昂贵和庞大的网络中，地铁网络总是在一个相对长的周期实现。因此，从动态的角度评价它们是重要的。在这些现有的模型中，每个模型都有一个发展的模式，虽然节点或边缘的变化可能是从一个步骤到另一个步骤，其作用机制并没有改变19,20。However,in order to respond to the dual standards, the coverage and the convenience, subway networks usually grow with different modes: expansion and intensification. One simple and possible mechanism of the two modes is shown in fig. 3. The mechanism will result into a typical ring and branch structure, which has been widely observed among worlds subway networks 21, however its growth procedure has never been clearly decomposed.然而，为了回应这种双标准，考虑到覆盖率和便利，地铁网络的生长通常具有不同的模式：扩展和深化。在这两种模式中的一个简单和可能的机制如图3所示，其机制将导致成典型的环和分支结构，这在世界地铁网络中被广为观察到21，但其生长过程从未明确地被分解过。In each step of the expanding mode, eight nodes will be added at the eight extremities of the network and eight edges will be added as well. In each step of the intensifying mode, eight edges will be added to form a most central circle all with 2-degree nodes.在不断扩大的模式中的每个步骤，8个节点将在8个网络的末端和8个边缘被添加。在加强模式的每个步骤中，8个边缘将以形成最中央的圆都带有2度的节点被添加。Obviously, the expanding mode enlarges the coverage of networks while the intensifying mode strengthens the connection within networks. More specifically, if the network grows continuously with the single mode, the expanding mode leads to the increase of ASPL, which means that the network becomes sparser and sparser. On the contrary, the intensifying mode leads to the decrease of ASPL and therefore makes the network more intense. 显然，当强化模式强化网络内的连接时，扩张模式扩大网络的覆盖范围。更具体地，如果网络通过单一模式持续增长，不断扩大的模式导致平均最短路径长度的增加，意味着网络变得越来越稀疏。相反，在加强模式导致平均最短路径长度的减少，因此使网络更加紧张。In reality, these two modes appear randomly and alternatively in the development of subway networks. Figure 4 shows the results of one random combination. Both the number of nodes and the number of edges increase where as the number of edge augments faster. The ASPL increase as well but with more observable variation. Meanwhile,it is noticeable that the ASPL grows almost linearly with the development of network, which is different to the phenomena in 25. 在现实中，在地铁网络的发展中，这两种