城市公交巴士复杂网络的实证与模拟研究
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摘要
城市公交巴士系统历史悠久,但并不完善,系统中依然存在着一些悬而未决的难题,需要从新的研究视角来进行分析,而当前新兴的复杂网络理论及其方法正好为这种研究需求提供了一个崭新平台。本课题应用复杂网络工具,通过实证分析、理论解析与计算机模拟的方式研究了城市公交巴士复杂网络的结构性质及其演化规律。
实证研究是本课题的基础研究工作。在实证阶段,作者利用三种映射方法将国内的四个城市:杭州、南京、北京、上海的公交巴士系统分别映射为基于线路相互关系、站点地理位置关系、站点换乘关系的公交巴士复杂网络。对这些复杂网络研究对象的分析,本研究实证获得了如下一些统计结果:1)相比于随机网络,三种空间下的城市公交巴士复杂网络都具有“小世界现象”,即小的特征路径长度和大的聚集系数,这表明仅需几步就能从一条线路换乘到另一条线路,或从一个站点到达另一个站点。2)用已有指标节点协调性系数、平均邻接节点度,实证获得的结果反映:城市公交巴士拓扑网络中的连接节点间存在着“正相关关系”的结论。本研究发现,该结论反映的是连接节点间的“伪正相关关系”。为此,本研究提出了统计指标“邻接节点度和”,用该指标去除噪声后,发现网络中连接节点间不存在相关关系。3)本研究应用邻接节点度和指标,挖掘出这些拓扑网络中节点随机连接的组织演化机制,而以映射获得的重边数为边权构造的加权网络中,统计结果显示,节点的连接与邻接节点度边权和之间存在着幂律标度的超线性相关关系;公交巴士加权网络和拓扑网络显示出截然不同的演化图景,这表明权重信息在城市公交巴士复杂网研究中至关重要。4)在城市公交巴士换乘关系复杂网络中,本研究获得了网络节点度分布的尾部具有漂移幂律的函数形式,且趋近于指数分布的统计结果。5)在城市公交巴士地理位置关系复杂网络中,本研究实证获得了网络弯头指数尾的节点度分布统计结果,并且获得了节点奇偶强度分布具有不同标度的指数分布结果。6)实证结果发现城市公交巴士线路关系复杂网络的统计结果比较有趣,其网络节点度和节点强度的补累积分布近似为一下斜直线,并且通过其各自网络的平均节点度与平均节点强度重新标度后,这些分布都具有近似统一的线性函数形式。
识别和模拟导致城市公交巴士复杂网连接分布结果的演化过程及机制的研究,是本论文的又一重要研究内容。国内四城市的公交巴士换乘关系复杂网络与许多实证复杂网络的节点度分布统计结果不同,其不存在节点连接无标度分布的规律,另外考虑到现实城市公交巴士换乘关系复杂网络的演化过程中既具有优选连接,也具有随机连接的事实,作者提出并采用了漂移幂律改进模型进行了模拟,该模型中引入了增长和具有初始吸引度的线性择优连接的两个重要机制;最后该改进模型从理论解析的角度重现了网络节点连接漂移幂律分布的尾部关系。在站点地理位置关系复杂网络中,根据网络节点度分布具有指数尾分布的统计结果,可知城市公交巴士地理位置关系复杂网络可以通过随机连接的增长网络模型来模拟,另外结合城市地理空间的限制,作者推测网络中公交线路应具有局域作用的自回避行走演化规律,考虑进这些要素,模型模拟结果确实重现了城市公交巴士地理位置关系复杂网中弯头指数尾节点度分布及节点奇偶强度不同标度指数分布的关键统计结果。
作者分别提出了竞争与合作统计指标及计算方法,然后对城市公交线路间的竞争与合作关系进行了定量分析与模拟研究。作者以南京公交系统为例,在规则网格中模拟了城市公交巴士换乘关系复杂网络及其运行过程;通过数值模拟,探讨了在不同网络节点线路权重的正相关、负相关或混合相关关系下引导生成的公交巴士复杂网络的整体合作与竞争程度,该模拟结果对揭示网络结构和网络竞争与合作程度的内在关联性具有一定的理论价值。
本论文对城市公交巴士复杂网络的研究取得了一些初步的成果,但有些结论还需要更多的城市公交巴士复杂网络实证结果及更深层次理论研究(如数学解析)的支持。深入地揭示城市公交巴士复杂网络中的组织演化规律,构建更加逼近现实的网络模型是作者研究的下一个目标。
Urban bus-transport systems are key infrastructures of modern cities, and they should be researched deeply. Their still existing defects even after long history evolutions need to be analyzed from a new viewpoint, which Complex Network can provide. This research on urban bus-transport networks (Abbr. BTNs) is carried out by empirical study, theoretical analysis and numerical simulation.
The author maps four urban bus-transport systems at the cities of Hangzhou, Nanjing, Beijing & Shanghai in China into BTNs by three methods corresponding to Spaces of the route relation, the stop geographical relation and the bus-transferring relation respectively. 1) Compared with random networks with same sizes, all the considered BTNs have“small world phenomena”with a large clustering coefficient and a small average shortest path length, i.e. only through several steps the passengers can transfer from one bus line to any other bus line, or from one stop to another. 2) The topological BTNs are identified as networks with“positive assortative correlation”, which are networks with“pseudo positive assortative correlations”in fact, by some common used measurements, hence Dn n( k ), named the average sum of the nearest neighbor degree of the same degree, is proposed to unveil the BTN’s underlying randomly linking correlation. 3) Further, the author uncovers that there is a common stochastic organization law in those topological BTNs identified by Dn n( k ), but their corresponding weighted BTNs (The multi-edges are considered as one’s link weight between a pair of vertices.) have positive assortative relations among the adjacent vertices following the power law, i.e. Dn wn( k )∝kβ, whereβ(>1) is constant, which means that a vertex with a larger degree connect preferentially with the others with a large edge-weight degree convergence; therefore, the topological BTNs and the weighted ones have different vertex linking laws, i.e. evolution mechanisms. These facts present qualitative arguments that confirm the importance of the weight and its weighted measurements since the topological measurements can not fully reveal the intrinsic coupling mechanisms among vertices. 4) In the bus-transferring space BTNs, each vertex follows a shifted power-law degree distribution, approaching to an exponential distribution. 5) In the stop geographical space BTNs, every vertex degree distribution has an exponential function form with lower head, and every vertex strength distribution has also an exponential law form but with asymmetric exponents between even and odd strengths. 6) The complementary cumulative distributions of degree and strength are approximate different lines, but they converge to one same line after scaled by their average degree or average strength respectively.
Further, the study is focused on the identification and simulation of the evolution law of the real-life BTNs. The statistical results of the four metropolis BTNs in the bus-transferring space show that the networks connectivity does not follow a scale-free degree distribution as most of the other networks do. The shifted power-law mended model proposed at present can analytically reproduce the real-life BTNs with the similar degree distributions tails. Two important ingredients: growth and linear preferential attachment with initial attractor, which are inferred by two facts of preference and random attachment principles in real-life evolutional BTNs, are considered in this model. From the statistical results, we know that in each empirical BTN in the stop geographical space, its vertex degree distribution has an exponential tail and lower head, and its vertex strength distribution has also an exponential law form with asymmetric exponents of even and odd strengths. Those empirical facts imply (infer) that those properties are induced by the constraints of geographical ground with local evolution rules of vertex randomly connected to its near-neighbor vertices as a route walks on stops without self-intersection. A simple model considered those points has been developed, and its simulation results consist with those key findings.
The study on the competition and cooperation relations among bus lines is quantitatively presented and the formulas of the measurements of competition and cooperation are given independently. In addition, based on the Nanjing BTN, one model is proposed to simulate its growth process and operation. To explore BTN’s competition and cooperation relations led by different correlations by the vertex bus line weights as positive relation, negative relation or mixing relation, many independent numerical simulations have been realized. The simulation results have a theoretical value for optimizing real-life urban bus-transport systems.
Finally, it must be claimed that the present study is only at its beginning stage, and the obtained results at present are expected to be verified in a larger scope of samples and more deeply theoretical studies. To unveil the underlying evolution law and to construct more accurate models of real-life BTNs are the author’s next goals.
实证研究是本课题的基础研究工作。在实证阶段,作者利用三种映射方法将国内的四个城市:杭州、南京、北京、上海的公交巴士系统分别映射为基于线路相互关系、站点地理位置关系、站点换乘关系的公交巴士复杂网络。对这些复杂网络研究对象的分析,本研究实证获得了如下一些统计结果:1)相比于随机网络,三种空间下的城市公交巴士复杂网络都具有“小世界现象”,即小的特征路径长度和大的聚集系数,这表明仅需几步就能从一条线路换乘到另一条线路,或从一个站点到达另一个站点。2)用已有指标节点协调性系数、平均邻接节点度,实证获得的结果反映:城市公交巴士拓扑网络中的连接节点间存在着“正相关关系”的结论。本研究发现,该结论反映的是连接节点间的“伪正相关关系”。为此,本研究提出了统计指标“邻接节点度和”,用该指标去除噪声后,发现网络中连接节点间不存在相关关系。3)本研究应用邻接节点度和指标,挖掘出这些拓扑网络中节点随机连接的组织演化机制,而以映射获得的重边数为边权构造的加权网络中,统计结果显示,节点的连接与邻接节点度边权和之间存在着幂律标度的超线性相关关系;公交巴士加权网络和拓扑网络显示出截然不同的演化图景,这表明权重信息在城市公交巴士复杂网研究中至关重要。4)在城市公交巴士换乘关系复杂网络中,本研究获得了网络节点度分布的尾部具有漂移幂律的函数形式,且趋近于指数分布的统计结果。5)在城市公交巴士地理位置关系复杂网络中,本研究实证获得了网络弯头指数尾的节点度分布统计结果,并且获得了节点奇偶强度分布具有不同标度的指数分布结果。6)实证结果发现城市公交巴士线路关系复杂网络的统计结果比较有趣,其网络节点度和节点强度的补累积分布近似为一下斜直线,并且通过其各自网络的平均节点度与平均节点强度重新标度后,这些分布都具有近似统一的线性函数形式。
识别和模拟导致城市公交巴士复杂网连接分布结果的演化过程及机制的研究,是本论文的又一重要研究内容。国内四城市的公交巴士换乘关系复杂网络与许多实证复杂网络的节点度分布统计结果不同,其不存在节点连接无标度分布的规律,另外考虑到现实城市公交巴士换乘关系复杂网络的演化过程中既具有优选连接,也具有随机连接的事实,作者提出并采用了漂移幂律改进模型进行了模拟,该模型中引入了增长和具有初始吸引度的线性择优连接的两个重要机制;最后该改进模型从理论解析的角度重现了网络节点连接漂移幂律分布的尾部关系。在站点地理位置关系复杂网络中,根据网络节点度分布具有指数尾分布的统计结果,可知城市公交巴士地理位置关系复杂网络可以通过随机连接的增长网络模型来模拟,另外结合城市地理空间的限制,作者推测网络中公交线路应具有局域作用的自回避行走演化规律,考虑进这些要素,模型模拟结果确实重现了城市公交巴士地理位置关系复杂网中弯头指数尾节点度分布及节点奇偶强度不同标度指数分布的关键统计结果。
作者分别提出了竞争与合作统计指标及计算方法,然后对城市公交线路间的竞争与合作关系进行了定量分析与模拟研究。作者以南京公交系统为例,在规则网格中模拟了城市公交巴士换乘关系复杂网络及其运行过程;通过数值模拟,探讨了在不同网络节点线路权重的正相关、负相关或混合相关关系下引导生成的公交巴士复杂网络的整体合作与竞争程度,该模拟结果对揭示网络结构和网络竞争与合作程度的内在关联性具有一定的理论价值。
本论文对城市公交巴士复杂网络的研究取得了一些初步的成果,但有些结论还需要更多的城市公交巴士复杂网络实证结果及更深层次理论研究(如数学解析)的支持。深入地揭示城市公交巴士复杂网络中的组织演化规律,构建更加逼近现实的网络模型是作者研究的下一个目标。
Urban bus-transport systems are key infrastructures of modern cities, and they should be researched deeply. Their still existing defects even after long history evolutions need to be analyzed from a new viewpoint, which Complex Network can provide. This research on urban bus-transport networks (Abbr. BTNs) is carried out by empirical study, theoretical analysis and numerical simulation.
The author maps four urban bus-transport systems at the cities of Hangzhou, Nanjing, Beijing & Shanghai in China into BTNs by three methods corresponding to Spaces of the route relation, the stop geographical relation and the bus-transferring relation respectively. 1) Compared with random networks with same sizes, all the considered BTNs have“small world phenomena”with a large clustering coefficient and a small average shortest path length, i.e. only through several steps the passengers can transfer from one bus line to any other bus line, or from one stop to another. 2) The topological BTNs are identified as networks with“positive assortative correlation”, which are networks with“pseudo positive assortative correlations”in fact, by some common used measurements, hence Dn n( k ), named the average sum of the nearest neighbor degree of the same degree, is proposed to unveil the BTN’s underlying randomly linking correlation. 3) Further, the author uncovers that there is a common stochastic organization law in those topological BTNs identified by Dn n( k ), but their corresponding weighted BTNs (The multi-edges are considered as one’s link weight between a pair of vertices.) have positive assortative relations among the adjacent vertices following the power law, i.e. Dn wn( k )∝kβ, whereβ(>1) is constant, which means that a vertex with a larger degree connect preferentially with the others with a large edge-weight degree convergence; therefore, the topological BTNs and the weighted ones have different vertex linking laws, i.e. evolution mechanisms. These facts present qualitative arguments that confirm the importance of the weight and its weighted measurements since the topological measurements can not fully reveal the intrinsic coupling mechanisms among vertices. 4) In the bus-transferring space BTNs, each vertex follows a shifted power-law degree distribution, approaching to an exponential distribution. 5) In the stop geographical space BTNs, every vertex degree distribution has an exponential function form with lower head, and every vertex strength distribution has also an exponential law form but with asymmetric exponents between even and odd strengths. 6) The complementary cumulative distributions of degree and strength are approximate different lines, but they converge to one same line after scaled by their average degree or average strength respectively.
Further, the study is focused on the identification and simulation of the evolution law of the real-life BTNs. The statistical results of the four metropolis BTNs in the bus-transferring space show that the networks connectivity does not follow a scale-free degree distribution as most of the other networks do. The shifted power-law mended model proposed at present can analytically reproduce the real-life BTNs with the similar degree distributions tails. Two important ingredients: growth and linear preferential attachment with initial attractor, which are inferred by two facts of preference and random attachment principles in real-life evolutional BTNs, are considered in this model. From the statistical results, we know that in each empirical BTN in the stop geographical space, its vertex degree distribution has an exponential tail and lower head, and its vertex strength distribution has also an exponential law form with asymmetric exponents of even and odd strengths. Those empirical facts imply (infer) that those properties are induced by the constraints of geographical ground with local evolution rules of vertex randomly connected to its near-neighbor vertices as a route walks on stops without self-intersection. A simple model considered those points has been developed, and its simulation results consist with those key findings.
The study on the competition and cooperation relations among bus lines is quantitatively presented and the formulas of the measurements of competition and cooperation are given independently. In addition, based on the Nanjing BTN, one model is proposed to simulate its growth process and operation. To explore BTN’s competition and cooperation relations led by different correlations by the vertex bus line weights as positive relation, negative relation or mixing relation, many independent numerical simulations have been realized. The simulation results have a theoretical value for optimizing real-life urban bus-transport systems.
Finally, it must be claimed that the present study is only at its beginning stage, and the obtained results at present are expected to be verified in a larger scope of samples and more deeply theoretical studies. To unveil the underlying evolution law and to construct more accurate models of real-life BTNs are the author’s next goals.
引文
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