EN中文

地球信息科学学报 >

2017 , Vol. 19 >Issue 10: 1279 - 1286

DOI: https://doi.org/10.3724/SP.J.1047.2017.01279

地球信息科学与应用技术

交通拥堵与预警信息交互传播动力学分析

  • 周艳 , 1, 2 ,
  • 李妍羲 , 1, * ,
  • 江荣贵 1 ,
  • 耿二辉 1
展开
  • 1. 电子科技大学 资源与环境学院, 成都 611731
  • 2. 电子科技大学 大数据研究中心,成都 611731
*通讯作者：李妍羲（1992- ）,女,重庆人,硕士生,主要从事地理信息系统应用。E-mail: liyanxi_gis@163.com

作者简介：周艳（1976- ）,女,陕西西安人,博士,副教授,主要从事地理信息系统应用和空间大数据分析。E-mail:

收稿日期: 2017-04-30

  要求修回日期: 2017-05-12

  网络出版日期: 2017-10-20

基金资助

国家重点研发计划项目（2016YFB0502300）

国家自然科学基金项目（41471332、41571392）

中央高校基本科研业务费专项资金资助（ZYGX2015J113）

收起

Dynamic Analysis of Interactive Transmission of Warning Information and Traffic Congestion

  • ZHOU Yan , 1, 2 ,
  • LI Yanxi , 1, * ,
  • JIANG Ronggui 1 ,
  • GENG Erhui 1
Expand
  • 1. School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China
  • 2. Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China
*Corresponding author: LI Yanxi, E-mail:

Received date: 2017-04-30

  Request revised date: 2017-05-12

  Online published: 2017-10-20

Copyright

《地球信息科学学报》编辑部 所有
Fold

摘要

城市交通拥堵问题已经成为当今世界许多城市发展过程中面临的一个严峻问题。针对这一问题,全空间信息系统通过对复杂、动态的交通拥堵过程进行多粒度抽象、多尺度建模和多层次综合分析,为解决城市交通拥堵提供了新的途径。当城市交通发生严重堵塞时,通常伴随着“道路拥堵”预警信息传播,用以影响人类的出行活动,从而在一定程度上影响交通拥堵传播。为了深入分析城市交通网络拥堵的动态演进过程,本文建立了交通拥堵传播的改进易感-感染-易感（susceptible-in fected-susceptible,SIS）的病毒传播模型,利用状态转移概率方法,基于多层复杂网络分析交通拥堵和预警信息交互传播的动力学行为特征,揭示预警信息传播对交通拥堵传播的影响。该方法不仅能够描述基于交通流传播特点的拥堵传播过程,而且能够描述交通网络中的预警信息传播过程。数字仿真实验表明,交通拥堵的传播过程与交通网络中的预警信息传播动力学之间存在关联关系。

关键词： 交通拥堵; 多层复杂网络; 病毒传播; 信息传播

本文引用格式

周艳 , 李妍羲 , 江荣贵 , 耿二辉 . 交通拥堵与预警信息交互传播动力学分析[J]. 地球信息科学学报, 2017 , 19(10) : 1279 -1286 . DOI: 10.3724/SP.J.1047.2017.01279

Abstract

The problem of urban traffic congestion has become a serious problem in the development of many cities in the world. To solve this problem, pan-spatial information system provides a new way of solving urban traffic congestion by multi-granularity abstracting, multi-scale modeling and multi-level comprehensive analysis of dynamic and complex traffic jam processes. In reality, the process of traffic congestion is usually accompanied by the dissemination of traffic warning information. Accordingly, when the competition occurs, which is generated by traffic congestion and the spreading of warning information in different network layers, the interplay between traffic congestion and warning information plays an important role. Thus, in order to study the interplay between information spreading and traffic congestion spreading, we constructed a multiplex network with road intersections or sites to analyze the interplay between information spreading and traffic congestion spreading. Firstly, we considered the effect of the surrounding nodes and proposed an improved SIS model. Then, based on the improved SIS model, we used the method of state transition probability to study the competing spreading processes of multiplex network. Finally, using the Monte Carlo method, we analyzed and simulated the traffic congestion threshold in both homogeneous network and heterogeneous network. This study indicates that the process of traffic congestion depends on dynamics of warning information spreading through transport network.

Key words： traffic congestion; multiplex network; epidemic spreading; information spreading

1 引言

城市交通拥堵问题已经成为当今世界许多城市发展过程中面临的一个严峻问题。交通拥堵不仅影响着城市交通系统的运行效率,还给城市发展和人类生活带来了诸多不便。城市交通系统是一个复杂巨系统,传统的分析理论与方法已无法满足城市交通系统的研究,全空间信息系统把现实世界抽象为由多粒度时空对象组成的数据世界,通过对现实世界中复杂、动态的交通拥堵过程进行多粒度抽象、多尺度建模和综合分析,为解决城市交通拥堵提供了新的途径[1-2]。
在交通拥堵传播领域,有学者通过研究人们对车辆路径的选择行为,发现不同网络拓扑结构和交通量产生率会影响交通拥堵的传播[3]。有研究分别针对匀质和异质交通需求,探讨了匀质及异质能力分配条件下的复杂交通网络的拥堵和效率情况[4]。根据实际交通传播的情况改进了中观交通流模型,并利用该模型分析了复杂网络上的交通传播动力学特征及传播规律[5]。部分研究网络基于拓扑结构与网络传输过程之间的关系,通过改变网络结构或改进路由算法的方法研究交通拥堵问题[6-8]。已有的研究主要集中在对网络拓扑结构、网络流量负荷与交通拥堵之间的关系进行分析,并没有考虑交通拥堵的传播过程。最新的研究通过建立考虑时间延迟影响的交通拥堵传播的SIS病毒传播模型,进而研究交通拥堵传播过程中的影响因素[9]。虽然是针对交通拥堵的传播过程,但是只单独研究了拥堵传播过程,没有考虑信息传播对拥堵传播的影响。然而,在现实生活中,交通拥堵传播过程往往会伴随着“道路拥堵”预警信息传播。这种“道路拥堵”预警信息可以通过人与人之间或者公共媒介等工具在人群中传播开来,进而出现交通拥堵传播与预警信息在网络中的交互传播。因此考虑交通拥堵-预警信息的全空间多层网络的交互传播是一个值得研究的重要问题。
综上所述,为了深入分析城市交通网络拥堵动态演化过程,本文根据交通流传播的特点,引入全空间信息系统多层次网络交互分析技术思想,建立了交通拥堵传播的改进SIS病毒传播模型,利用状态转移概率的方法,研究多层网络中交通拥堵传播和预警信息传播相互交互动力学。基于无标度网络和小世界网络对模型进行仿真,进一步比较分析了相关影响因素的作用规律,可为交通拥堵的管理或控制策略的制定提供一定的参考。

2 基于状态概率转移的交通拥堵-预警信息交互模型

2.1 基于交通拥堵传播的改进SIS病毒传播模型分析

经典的SIS病毒传播模型一般用来描述痊愈后的个体不能拥有免疫能力的疾病,比如流行性感冒等。因此,在SIS病毒传播模型中,节点被划分为两类：易感节点和感染节点。在病毒传播过程中,当感染节点遇到易感节点时,会以感染率β把传染病传给易感节点。同时,由于感染后的个体自身的安全机制的作用,将以恢复率δ转变为易感节点。而且,易感节点一旦被感染,将会充当感染节点的角色继续传播病毒。
与SIS病毒传播过程相比,交通拥堵传播具有相似的传播过程,但由于交通系统自身的复杂特性,其传播过程又具有典型的多尺度交互影响特点（节点-路口-路段-网络）。在交通拥堵传播过程中,当拥堵节点以恢复率δ转变为畅通节点时,其恢复过程与下游道路的路况有关,交叉口下游的畅通道路越多,拥堵消散过程耗时越短,而感染节点的恢复过程与周围的节点的状态无关。
因此,在改进的SIS病毒传播模型中,节点被划分为2类：畅通节点（对应易感节点）和拥堵节点（对应感染节点）。当拥堵传播率β超过一定阈值时,拥堵节点会以传播率β使周围的畅通节点变为拥堵节点;同时,在拥堵消散过程中,拥堵节点会因为周围节点的交通状况,以消散率δ转变为畅通节点。

2.2 交通拥堵-预警信息交互模型分析

由于交通拥堵传播过程往往会伴随着“道路拥堵”预警信息传播,这使得具有多尺度交互影响特点的交通拥堵传播过程变得更加复杂,因此本文借鉴全空间信息系统多层次网络交互分析思想,引入复杂网络技术理论,对交通拥堵与信息传播过程进行多粒度抽象（节点-路口-路段-网络）,同时构建出交通拥堵-预警信息多层网络模型。该多层网络包含两层复杂网络,一层是演化交通拥堵传播过程的城市交通网络,一层是描述“道路拥堵”预警信息传播的通信网络。在城市交通网络中,道路交叉口或站点对应节点,连接它们的道路对应边,其中采用改进的SIS病毒传播模型演化交通拥堵在网络中的传播。
在信息通信网络中,节点集与城市交通网络的节点集相同,边则代表节点之间是否能进行正常通信。对信息通信网络,采用正常-预警-正常（normal-warning-normal,NWN）信息传播模型描述“道路拥堵”预警信息在网络中的传播。在NWN信息传播模型中,网络节点具有2种形式：具有并能转发预警信息的节点（即节点的状态为W）和没有预警信息或通信受限的节点（即节点的状态为N）。在预警信息传播过程中,当驾驶人员获得“道路拥堵”预警信息时,往往会考虑重新选择路线,从而减少了进入拥堵路段的车流量,加快拥堵消散,但是,没有接受到预警信息的个体则不会采取措施来减少拥堵风险。假设预警信息的主要来源有2个方面：① 来源于信息通信层中产生并发出了预警信息的节点,即没有预警信息的节点与发出预警信息的节点进行通信,以概率λ接受到预警信息并转化为具有预警信息的节点;② 来源于交通网络层中已拥堵的节点,即交通网络层中已拥堵的节点在通信网络层中自发地转为具有预警信息的节点。同时,随着道路交通由拥堵状态转为畅通状态,预警信息也逐渐停止传播,从而导致具有预警信息的节点以概率μ变为无预警信息的节点。
在上述交通拥堵-预警信息交互传播模型中,假设未被预警的交通畅通路口发生拥堵的概率为βN,拥堵消散的概率为δN;而被预警的交通畅通路口发生拥堵的概率为βW,拥堵消散的概率为δW。已知被预警的交通畅通路口发生拥堵的概率一般会小于未被预警的交通畅通路口,同时,被预警的交通拥堵路口比未被预警的交通拥堵路口的拥堵消散过程耗时更少,因此,设被预警的交通畅通路口发生拥堵的概率相对于未被预警的交通畅通路口以因子γ（0≤γ≤1）倍相应地发生交通拥堵,即βW=γβN,而未被预警的交通拥堵路口相对于被预警的交通拥堵路口以因子θ（0≤θ≤1）倍相应地进行拥堵消散过程,即δN=θδW。特例,γ=0表示被预警的交通畅通路口不会发生拥堵,同理,θ=0表示未被预警的交通拥堵路口在短时间内不会改变拥堵状态。
依据上述交通拥堵-预警信息交互传播机制,多层网络中的节点可分为3类：被预警的交通畅通路口、被预警的交通拥堵路口和未被预警的交通畅通路口,其对应的3种状态分别为：预警-易感（Warning-Susceptible,WS）状态、预警-感染（Warning-Infected,WI）状态和正常-易感（Normal-Susceptible,NS）状态。由于在动力学交互过程中,假设未被预警的交通拥堵路口立即转化为被预警的交通拥堵路口,因此在描述交通拥堵-预警信息交互模型中,正常-感染（Normal-Infected,NI）状态可被忽略。综上所述,交通拥堵-预警信息交互传播模型（Susceptible-Infected-Susceptible and Normal-Warning-Normal,SIS-NWN）中不同类型节点的状态转化示意图,如图1所示,其中涉及到的主要符号及具体描述见表1。
Fig. 1 Transition probability diagram for the nodes𠈙 states in the two-layer SIS-NWN networks

图1 多层网络中交通拥堵-预警信息模型的节点状态转化示意图

Tab. 1 The main notations and descriptions

表1 主要的符号及描述

符号 描述
λ 节点由正常状态（N）转化为预警状态（W）的概率
μ 节点由预警状态（W）转化为正常状态（N）的概率
βN 处于正常状态（N）的节点发生交通拥堵的概率
βW 处于预警状态（W）的节点发生交通拥堵的概率
δN 处于正常状态（N）的节点发生拥堵后,拥堵消散的概率
δW 处于预警状态（W）的节点发生拥堵后,拥堵消散的概率
假设多层网络中每层复杂网络的节点总数均为M,用A=[aij]∈RM×M和B=[bij]∈RM×M分别表示信息通信网络和城市交通网络的邻接矩阵,当节点i和节点j相邻时,值为1,反之为0。初始时刻在网络中随机选择一个节点i作为具有拥堵信息的交通拥堵节点。设 p i WI t 、 p i WS t 和 p i NS t 分别为t时刻节点i处于WI、WS和NS状态的概率,由于该交通拥堵-预警信息交互传播模型满足连续时间的马尔科夫过程,因此其满足归一化条件（式（1））：
p i WI t + p i WS t + p i NS t = 1 （1）
根据Chakrabarti等[10]的方法,结合图1,可以利用节点i在t时刻处于各个状态的概率来描述各个节点的动力学过程,从而建立交通拥堵传播动力学方程,例如从图1中可知,t+1时刻处于NS状态的节点的概率与t时刻NS状态的节点没有转化为其它状态的概率、WI状态的节点转化为NS状态的概率以及WS状态的节点转化为NS状态的概率有关,因此t+1时刻节点i处于NS状态的概率 p i NS t + 1 计算公式如式（2）,其中 p i NS t 1 - r i t + 1 - q i N t 为t时刻状态为NS的节点保持状态不变的概率; p i WI t f i N t 为t时刻状态为WI的节点发生拥堵消散转化到NS状态的概率; p i WS t μ 为t时刻状态为WS的节点停止传播预警信息,从而转化到NS状态的概率。同理可以分析计算得到式（3）和（4）。
p i NS t + 1 = p i NS t 1 - r i t + 1 - q i N t + p i WI t f i N t + p i WS t μ （2）
p i WS t + 1 = p i WS t 1 - q i W t + 1 - μ + p i WI t f i W t + p i NS t r i t （3）
p i WI t + 1 = p i WI t 1 - f i W t + 1 - f i N t + p i WS t q i W t + p i NS t q i N t （4）
其中,ri(t)为通信网络层中节点i受到具有预警信息的邻居点影响接收到预警信息的概率,计算见式（5）; q i W t 为在具有预警信息的拥堵节点影响下节点由畅通转为拥堵的概率,计算见式（6）,反之为 q i N t ,计算见式（7）;同理, f i W t 为在具有预警信息条件下的发生拥堵消散的概率,计算见式（8）,反之为 f i N t ,具体计算见式（9）。
r i t = 1 - ∏ j = 1 M 1 - λ a ji p j W t ] （5）
q i W t = 1 - ∏ j = 1 M 1 - β W b ji p j WI t ] （6）
q i N t = 1 - ∏ j = 1 M 1 - β N b ji p j WI t ] （7）
f i W t = 1 - ∏ j = 1 M 1 - δ W b ji p j WS t ] （8）
f i N t = 1 - ∏ j = 1 M 1 - δ N b ji p j NS t ] （9）
其中, p j W t = p j WI t + p j WS t （10）

3 阈值分析

根据上面建立的交通拥堵-预警信息交互传播动力学方程可以看出,影响交通拥堵传播的参数较多,因此需要通过阈值分析找到其中具有重要作用的影响参数。
当t→∞时,3种状态NS、WS及WI节点的总数分 别 N NS = ∑ i = 1 M p i NS ∞ , N WS = ∑ i = 1 M p i WS ∞ , N WI = ∑ i = 1 M p i WI ∞ 。 采用稳态分析方法,可以利用这组动力学方程求得传播临界值。
式（2）-（4）是一个非线性动力学系统,设系统初始节点的值为0,可以通过雅可比矩阵式（11）来分析式（7）在初始点的局部稳定性：
DF | 0,0 = β N B - δ N B 0 M λA 1 - μ I M + λA （11）
式中：B=[bij]M×M,A=[aij]M×M,IM为M阶单位矩阵。当满足 max β N B - δ N B ， 1 - μ I M + λA < 1 时,初始节点局部稳定,从而可以得到式（12）：
β N < 1 Λ max B + δ N ， λ < μ Λ max A （12）
式中： Λ max B ， Λ max A 分别是B矩阵和A矩阵的最大特征值。由式（12）可以看出,参数βN和δN为影响力较大的参数,其取值的大小会极大地影响交通拥堵传播,同时,矩阵B和矩阵A的最大特征值也会影响交通拥堵传播。因此,交通拥堵的传播过程不仅与交通拥堵传播阈值和交通拥堵消散阈值有关,而且与交通网络中的预警信息传播动力学有关。

4 数值仿真

为了验证上述状态概率方程分析的传播临界值的正确性以及进一步分析影响参数在交通拥堵传播过程中的作用,本文以BA无标度网络和WS小世界网络作为复杂网络城市交通网络的拓扑结构模型[9,11-12],并假设双层网络中的两层网络均为同一个BA无标度网络或WS小世界网络,设网络规模均为M=1000。基于Monte Carlo仿真,在交通拥堵传播和预警信息传播的初始时刻,从交通网络层中随机选择一个节点作为交通拥堵节点,同时令该随机选择的节点在信息通信层中作为最先具有“道路拥堵”预警信息的节点。多层网络中拥堵节点的稳态密度为 p I = ∑ p i I / M = ∑ p i WI / M ,具有预警信息节点的稳态密度为 p W = ∑ p i W / M = ∑ ( p i WI + p i WS ) / M 。
由βW=γβW,当γ=0时表示具有预警信息的节点不会发生拥堵,即βW=0;当γ=1时表示具有预警信息的节点没有采取措施降低拥堵产生的概率,即βW=βN。图2表示在无标度网络和小世界网络下,三种不同交通拥堵传播模型（即γ=0、γ=0.5、γ=1）的拥堵稳态密度与拥堵传播率β=βN的关系,设预警信息传播率为λ=0.2,预警信息消失率为μ=0.4,具有预警信息的交通拥堵消散率为δW=0.2,倍数θ=0.2。图2显示,基于多层网络的拥堵-预警交互传播模型增强了交通拥堵传播临界值,显著降低了交通拥堵爆发规模,并且具有预警信息的节点均不发生拥堵的拥堵-预警交互模型（γ=0）,明显比具有预警信息的节点以βW=γβN概率发生拥堵的交互模型在降低交通拥堵爆发的风险上,更加有效地抑制了拥堵在路网中的传播,降低了交通拥堵最终爆发规模。
Fig. 2 The size of infected nodes pI is shown as a function of infectivity β of three kinds of traffic congestion models in Watts-Strogatz model and Barabasi-Albert model, respectively

图2 在无标度网络和小世界网络中3种交通拥堵模型的pI随β的变化图

Fig. 3 The size of infected nodes pI is shown as a function of infectivity δ of three kinds of traffic congestion models in Watts-Strogatz model and Barabasi-Albert model, respectively

图3 在无标度网络和小世界网络中3种交通拥堵模型的pI随δ的变化图

Fig. 4 Monte Carlo simulations of the two-layer SIS-NWN networks in Watts-Strogatz model and Barabasi-Albert model.The size of infected nodes pI is shown as a function of infectivity δW

图4 在无标度网络和小世界网络中不同δW值下的交通拥堵-预警信息交互模型

由δN=θδW,当θ=0时表示未被预警的节点在短时间内不会发生拥堵消散,即δN=0;当θ=1时表示交通拥堵消散的过程均受到预警信息传播的影响,即δN=δW。图3表示在无标度网络和小世界网络下,3种不同交通拥堵传播模型（即θ=0、θ=0.5、θ=1）的拥堵稳态密度与拥堵消散率δ=δW的关系,设预警信息传播率为λ=0.2,预警信息消失率为μ=0.4,具有预 警信息的交通拥堵消散率为βN=0.6,倍数γ=0.4。根据图3的仿真结果可知,具有预警信息的交通拥堵消散过程能显著降低交通拥堵的爆发规模,特别是当交通拥堵消散过程均受到预警信息传播的影响时（θ=1）,预警信息的传播对拥堵的爆发规模影响更大。
在实际路网中,交通拥堵的爆发规模不仅与拥堵路口处的交通拥堵传播临界值有关,还与该路口的拥堵消散能力有关,并且接受到预警信息的路口会提高抗拥堵能力。图4表示,在具有预警信息的条件下,不同拥堵消散概率δW=0.2、0.4、0.6、0.8对拥堵爆发规模的影响。从图中可以看出,在无标度网络和小世界网络下,预警信息对拥堵路口的消散能力影响程度越大,拥堵传播阈值越大,拥堵爆发规模越小。
Fig. 5 The relationship between pI, pW and β under differentvalues in Watts-Strogatz model and Barabasi-Albert model

图5 在无标度网络和小世界网络中不同λ值下的pI、pW与β之间的关系

图5表示不同的预警信息传播率λ=0.2、0.4、0.6、0.8下,拥堵传播规模pI、信息传播规模pW与交通拥堵传播率β之间的关系。设具有预警信息的节点降低拥堵发生的程度为γ=0.4,预警信息消失率为μ=0.4,具有预警信息的交通拥堵消散率为δW=0.2,倍数θ=0.2。图5显示,在无标度网络和小世界网络中,随着预警信息传播率λ的增大,拥堵传播规模 和信息传播规模同时降低。这意味着预警信息在网络中的蔓延减缓了拥堵的传播,减小了拥堵爆发规模。

5 结论

在实际生活中,当道路发生交通拥堵时,拥堵的传播与消散过程不仅与拥堵处周围的道路路况有关,还会受到“道路拥堵”预警信息传播的影响。同时,由于实际的交通系统通常是由多个相互作用且相互依赖的复杂网络组成,因此本文根据交通流传播的特点,引入全空间信息系统多层次网络交互分析技术思想,对复杂、动态的交通拥堵过程进行节点-路口-路段-网络的多粒度抽象和多尺度建模,建立了交通拥堵传播的改进SIS病毒传播模型,并利用状态转移概率的方法,构建多层网络中交通拥堵传播和预警信息传播的交互动力学模型。在该模型中,通过考虑拥堵处周围路况对拥堵消散过程的影响而改进的SIS病毒传播模型,用以描述城市交通网络层中的交通拥堵传播过程,并且采用NWN信息传播模型描述信息通信层中的预警信息传播过程。针对本文所提出的交通拥堵-预警信息模型,通过数学推导和数值仿真相结合的方法,发现并证明了交通拥堵的传播过程不仅与交通拥堵传播阈值和交通拥堵消散阈值有关,而且与交通网络中的预警信息传播动力学有关。同时,仿真实验结果还表明,“道路拥堵”预警信息在网络中的传播能在一定程度上减缓交通拥堵的传播,从而降低拥堵爆发的规模。多层网络中交通拥堵传播和预警信息交互传播的研究,不仅为研究城市的交通拥堵提供了一种新的视角,同时,也为全空间信息系统多层次网络交互传播分析技术研究提供了一定的应用参考。

The authors have declared that no competing interests exist.

参考文献

原文顺序 | 文献年度倒序 | 文中引用次数倒序
[1]
周成虎. 全空间地理信息系统展望[J].地理科学进展,2015,34(2):129-131.地理信息系统作为一门空间科学,以其独特的空间观点和空间思维,从空间相互联系和相互作用出发,揭示各种事物与现象的空间分布特征和动态变化规律。本文从地理信息系统所研究的空间对象出发,对地理信息系统发展新方向提出思考：①从地球空间拓展到宇宙空间,需要构建宇心坐标系和宇宙GIS、月球GIS等;②从室外空间延伸到室内空间,需要发展室内GIS,并拓展到水下空间和地下空间;③从宏观到微观空间,可以发展面向游戏的体育GIS、面向生命健康管理的人体GIS等;④面向大数据时代,发展大数据空间解析的理论和方法,贡献于大数据科学的发展。

DOI

[ Zhou C H.Prospects on pan-spatial information system[J]. Progress in Geography, 2015,34(2):129-131. ]

[2]
华一新. 全空间信息系统的核心问题和关键技术[J].测绘科学技术学报,2016,33(4):331-335.分析了空间信息系统的研究现状和存在问题,阐明了全空间信息系统的基本概念和基本特征;提出了基于多粒度时空对象构建全空间信息系统的技术路线,明确了需要研究解决的科学问题和关键技术;提出了全空间信息系统与智能设施管理的主要研究内容,指出预期的研究效益。

DOI

[ Hua Y X.The core problems and key technologies of pan-spatial information system[J]. Journal of Geomatics Science and Technology, 2016,33(4):331-335. ]

[3]
Wu J, Sun H, Gao Z.Dynamic urban traffic flow behavior on scale-free networks[J]. Physica A: Statistical Mechanics and its Applications, 2008,387(2):653-660.In this paper, we propose a new dynamic traffic model (DTM) for routing choice behaviors (RCB) in which both topology structures and dynamical properties are considered to address the RCB problem by using numerical experiments. The phase transition from free flow to congestion is found by simulations. Further, different topologies are studied in which large degree distribution exponents may alleviate or avoid the occurrence of traffic congestion efficiently. Compared with random networks, it is also found that scale-free networks can bear larger volume of traffic by our model. Finally, based on the concept of routing guide system (RGS), we give a dynamic traffic control model (DTCM) by extending DTM. And we find that choosing an appropriate η η mathContainer Loading Mathjax -value can enhance the system’s capacity maximally. We also address several open theoretical problems related to the urban traffic network dynamics and traffic flow.

DOI

[4]
Zheng J F, Zhu Z H, Du H M, et al.Congestion and Efficiency in Complex Traffic Networks[J]. International Journal of Modern Physics C, 2013,24(10):1350072.This paper investigates the degree of congestion and efficiency in complex traffic networks, by introducing congestion effects, which can be described by flow-based link cost functions. Different network topologies including random networks, small-world networks and scale-free networks are explored. The impact of different distributions of capacity and origin-destination traffic demand on the degree of congestion and efficiency in complex networks is mainly studied. A phase transition from free flow state to traffic jams can be uncovered. The relationship between congestion and efficiency in complex networks is also discussed.

DOI

[5]
李树彬,吴建军,高自友,等.基于复杂网络的交通拥堵与传播动力学分析[J].物理学报,2011,60(5):140-148.本文运用改进的中观交通流模型,研究了网络拓扑结构对交通拥堵的影响,进而分析复杂网络上的交通传播动力学特征和传播规律.结论有助于提出消除交通拥堵的有效控制策略以及交通规划的合理方案.

[ Li S B, Wu J J, Gao Z Y, et al.The analysis of traffic congestion and dynamic propagation properties based on complex network[J]. Acta Phys Sin, 2011,60(5):140-148. ]

[6]
Liu G, Gao P C, Li Y S.Transport capacity limit of urban street networks[J]. Transactions in GIS, 2017,21(3):575-590.Abstract Network transport is an important aspect of geographical information science, transportation, complex networks, etc. Previous studies have shown that the transport capacity of street networks can be enhanced by improving routing algorithms. However, the upper throughput limit of street networks is unknown in detail. This article studies the transport process of networks and finds that any connected network has a maximum throughput depending on the topological and structural properties of the network. Based on this, the maximum throughput of street networks is obtained. Experiments show that when the street network remains unchanged, the maximum throughput of the street network is limited and is dependent on road capacity and average path length, regardless of adopted routing algorithms. Our findings suggest that the throughput of networks can be improved by increasing node capacity or decreasing average path length, but the maximum transport capacity of the network cannot be greater than the ratio of the sum of all the nodes' capacities to the average path length of the network, no matter what routing strategies are adopted. This study is expected to be a starting point for more sophisticated research in network transport, such as evaluating the inherent throughput of an urban street network.

DOI

[7]
Liu G, Li Y, Yang J, et al.Gravitational field routing strategy considering the distribution of traffic flow[J]. International Journal of Geographical Information Science, 2014,28(1):39-55.Traffic flow transmission is a constantly important aspect of complex networks, geographical information science, and other science and engineering fields. Previous studies have shown that vehicle flow is more strongly correlated with morphological properties of streets than those of axial lines. In addition, street-based topological representations are more suitable for vehicle flow prediction, as well as more memory-oriented and global in nature. In this study, we construct a dual graph to represent the street鈥搒treet relationship and propose a routing strategy for networks on the basis of gravitational field theory. We aim to diminish traffic congestion and enhance the transmission performance of networks. We borrow from gravitational field theory in establishing a gravitational field stimulated by a node in packet transmission and in defining the corresponding gravitational field equation. On the basis of this study, we present a mathematical model and a routing strategy. Experimental results indicate that compared with the shortest path routing strategy, the proposed method considerably enhances network capacity and effectively balances network traffic flow, especially for congested networks. We achieve critical gravitation that can always maximize network capacity, regardless of the values of other parameters.

DOI

[8]
刘刚,李永树.基于引力约束的复杂网络拥塞问题研究[J].物理学报,2012,61(10):108901.如何在保证网络传输效率的同时提高网络的吞吐量是目前研究的主要问题. 通过研究节点对数据包传递过程的引力作用,提出了一种具有引力约束的路由算法. 为检验算法的有效性,通过引入一个状态参数H, 利用由稳态到拥塞状态的指标流量相变值来度量网络的吞吐量, 同时利用数据包的最大传输时间〈<i>T</i><sub>max</sub>〉 与平均传输时间 〈<i>T</i><sub>avg</sub>〉来分析网络的传输效率. 针对算法在不同引力约束条件下的路由情况进行了仿真.仿真结果表明, 若数据传递过程只考虑路径长度最短,则会导致网络吞吐量较低且流量分布极不均匀; 若只顾及等待时间最短,会导致传输路径过度迂回且大部分节点都会陷入拥塞状态; 同时考虑路径长度和等待时间的引力作用并选取适当引力的节点进行传递, 可以显著提高网络吞吐量并缓解网络的拥塞程度.

DOI

[ Liu G, Li Y S.Study on the congestion phenomena in complex network based on gravity constraint[J]. Acta Physica Sinica, 2012,61(10):108901.]

[9]
张俊锋,马昌喜,吴芳,等.复杂城市交通网络拥堵传播的改进 SIS 模型[J].交通运输研究,2015,1(6):20-25.为深入分析城市交通网络拥堵动态演进过程,建立了交通拥堵传播的改进SIS模型(传染病模型)。模型根据目标节点自身受随机因素的影响、其邻居节点的状态和影响能力以及不同状态节点间的耦合强度,动态计算目标节点由畅通变为拥堵又恢复畅通的概率,并进一步考虑了不同交通状态的传播时间对拥堵传播的影响。基于BA(Barabási-Albert)无标度网络对传播过程进行仿真,拥堵随时间的演化与相关研究一致,验证了模型的有效性。仿真结果表明:根据作用节点属性的不同,随机因素对拥堵的初始规模、传播速度及传播稳定状态的阻塞水平具有不同的影响能力;不同状态节点间的相互作用对拥堵传播具有重要作用;畅通状态与拥堵状态平均传播时间的比值对拥堵传播的影响存在阈值;不同状态传播时间的波动性对拥堵传播速度、平衡态阻塞水平具有一定影响。

DOI

[ Zhang J F, Ma C X, Wu F, et al.Improved SIS model of congestion propagation of complex urban traffic network[J]. Transport Research, 2015,1(6):20-25. ]

[10]
Chakrabarti D, Wang Y, Wang C, et al.Epidemic thresholds in real networks[J]. ACM Transactions on Information and System Security (TISSEC),2008,10(4):1.How will a virus propagate in a real network&quest; How long does it take to disinfect a network given particular values of infection rate and virus death rate&quest; What is the single best node to immunize&quest; Answering these questions is essential for devising network-wide strategies to counter viruses. In addition, viral propagation is very similar in principle to the spread of rumors, information, and &#8220;fads,&#8221; implying that the solutions for viral propagation would also offer insights into these other problem settings. We answer these questions by developing a nonlinear dynamical system (NLDS) that accurately models viral propagation in any arbitrary network, including real and synthesized network graphs. We propose a general epidemic threshold condition for the NLDS system: we prove that the epidemic threshold for a network is exactly the inverse of the largest eigenvalue of its adjacency matrix. Finally, we show that below the epidemic threshold, infections die out at an exponential rate. Our epidemic threshold model subsumes many known thresholds for special-case graphs (e.g., Erd&#246;s--R&#233;nyi, BA powerlaw, homogeneous). We demonstrate the predictive power of our model with extensive experiments on real and synthesized graphs, and show that our threshold condition holds for arbitrary graphs. Finally, we show how to utilize our threshold condition for practical uses: It can dictate which nodes to immunize; it can assess the effects of a throttling policy; it can help us design network topologies so that they are more resistant to viruses.

DOI

[11]
赵军. 基于小世界模型的交通网络拥堵状态研究[J].自动化仪表,2015,36(6):15-18.在对海量数据进行分析和利用的同时，数据挖掘作为一种首选的工具已经普遍应用到各个领域中。为了解决交通网络中车辆拥堵的状态，在利用复杂网络中的小世界模型建立交通网络模型时，借助数据挖掘中的谱聚类方法对交通网络的拥堵状态进行分析，通过计算道路的平均拥堵时间控制交通灯的放行时间，使得整个交通网络不出现异常拥堵情况。采用NetLogo 5.0.3作为试验平台，对模拟交通网络进行分析，成功实现对交通流的调节，避免了长时间拥堵情况的发生。

DOI

[ Zhao J.Study on the congestion status of transportation network based on small world model[J]. Process Automation Instrumentation, 2015,36(6):15-18. ]

[12]
Wu J, Sun H, Gao Z.Capacity assignment model to defense cascading failures[J]. International Journal of Modern Physics C, 2009,20(7): 991-999.How to alleviate the damages of cascading failures triggered by the overload of edges/nodes is common in complex networks. To describe the whole cascading failures process from edges overloading to nodes malfunctioning and the dynamic spanning clustering with the evolvement of traffic flow, we propose a capacity assignment model by introducing an equilibrium assignment rule of flow in artificially created scale-free traffic networks. Additionally, the capacity update rule of node is given in this paper. We show that a single failed edge may undergo the cascading failures of nodes, and a small failure has the potential to trigger a global cascade. It is suggested that enhancing the capacity of node is particularly important for the design of any complex network to defense the cascading failures. Meanwhile, it has very important theoretical significance and practical application worthiness in the development of effective methods to alleviate the damage of one or some failed edges/nodes.

DOI

[13]
刘权辉,王伟,唐明.多层耦合网络传播综述[J].复杂系统与复杂性科学,2016,13(1):48-57.简要介绍多层耦合网络上传播动力学方面的阶段性研究进展以及存在的一些问题,主要关注的内容:多层耦合网络上的生物传播、社会传播、生物-社会耦合传播及多层耦合网络面临的一些挑战性问题.这些阶段性的研究成果从多层耦合网络的新角度加深了我们对真实传播过程及其机制的理解.能更好地控制疾病传播和减少它对人类的危害,深入探讨相关问题将有助于明确下进一步研究的方向.

DOI

[ Liu Q H, Wang W, Tang M.A review on the spreading of multilayer coupled networks[J]. Complex Systems & Complexity Science, 2016,13(1):48-57. ]

[14]
鲁延玲. 基于人类行为的复杂网络病毒传播研究[D].南京:南京邮电大学,2015.

[ Lu Y L.Epidemic spreading in complex networks based on human behaviors[D]. Nanjing: Nanjing University of Posts and Telecommunications, 2015. ]

[15]
Salehi M, Sharma R, Marzolla M, et al.Spreading processes in multilayer networks[J]. IEEE Transactions on Network Science and Engineering, 2015,2(2):65-83.Several systems can be modeled as sets of interconnected networks or networks with multiple types of connections, here generally called multilayer networks. Spreading processes such as information propagation among users of online social networks, or the diffusion of pathogens among individuals through their contact network, are fundamental phenomena occurring in these networks. However, while information diffusion in single networks has received considerable attention from various disciplines for over a decade, spreading processes in multilayer networks is still a young research area presenting many challenging research issues. In this paper, we review the main models, results and applications of multilayer spreading processes and discuss some promising research directions.

DOI

[16]
Guo Q, Jiang X, Lei Y, et al.Two-stage effects of awareness cascade on epidemic spreading in multiplex networks[J]. Physical Review E, 2015,91(1):012822.DOI: http://dx.doi.org/10.1103/PhysRevE.91.012822

DOI PMID

[17]
Wang W, Tang M, Yang H, et al.Asymmetrically interacting spreading dynamics on complex layered networks[J]. ArXiv preprint arXiv, 2014:14051905Abstract: The spread of disease through a physical-contact network and the spread of information about the disease on a communication network are two intimately related dynamical processes. We investigate the asymmetrical interplay between the two types of spreading dynamics, each occurring on its own layer, by focusing on the two fundamental quantities underlying any spreading process: epidemic threshold and the final infection ratio. We find that an epidemic outbreak on the contact layer can induce an outbreak on the communication layer, and information spreading can effectively raise the epidemic threshold. When structural correlation exists between the two layers, the information threshold remains unchanged but the epidemic threshold can be enhanced, making the contact layer more resilient to epidemic outbreak. We develop a physical theory to understand the intricate interplay between the two types of spreading dynamics.

DOI PMID

[18]
Massaro E, Bagnoli F.Epidemic spreading and risk perception in multiplex networks: A self-organized percolation method[J]. Physical Review E, 2014,90(5):052817.In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we assume to be related to the fraction of infected neighbours, as introduced by Bagnoli et al., PRE 76:061904 (2007). We re-derive previous results using a self-organized method, that automatically gives the percolation threshold in just one simulation. We then extend the model to multiplex networks considering that people get infected by contacts in real life but often gather information from an information networks, that may be quite different from the real ones. The similarity between the real and information networks determine the possibility of stopping the infection for a sufficiently high precaution level: if the networks are too different there is no mean of avoiding the epidemics.

DOI PMID

[19]
巩永旺. 考虑个体行为的复杂网络病毒传播研究[D].南京:南京邮电大学, 2014.

[ Gong Y W.Study on epidemic spreading in complex networks considering individuals’ behaviors. Nanjing: Nanjing University of Posts and Telecommunications, 2014. ]

[20]
Zhao D, Li L, Peng H, et al.Multiple routes transmitted epidemics on multiplex networks[J]. Physics Letters A, 2014,378(10):770-776.This letter investigates the multiple routes transmitted epidemic process on multiplex networks. We propose detailed theoretical analysis that allows us to accurately calculate the epidemic threshold and outbreak size. It is found that the epidemic can spread across the multiplex network even if all the network layers are well below their respective epidemic thresholds. Strong positive degree鈥揹egree correlation of nodes in multiplex network could lead to a much lower epidemic threshold and a relatively smaller outbreak size. However, the average similarity of neighbors from different layers of nodes has no obvious effect on the epidemic threshold and outbreak size.

DOI

[21]
Granell C, G mez S, Arenas A. Dynamical interplay between awareness and epidemic spreading in multiplex networks[J]. Physical review letters, 2013,111(12):128701.We present the analysis of the interrelation between two processes accounting for the spreading of an epidemic, and the information awareness to prevent its infection, on top of multiplex networks. This scenario is representative of an epidemic process spreading on a network of persistent real contacts, and a cyclic information awareness process diffusing in the network of virtual social contacts between the same individuals. The topology corresponds to a multiplex network where two diffusive processes are interacting affecting each other. The analysis using a microscopic Markov chain approach reveals the phase diagram of the incidence of the epidemics and allows us to capture the evolution of the epidemic threshold depending on the topological structure of the multiplex and the interrelation with the awareness process. Interestingly, the critical point for the onset of the epidemics has a critical value (metacritical point) defined by the awareness dynamics and the topology of the virtual network, from which the onset increases and the epidemics incidence decreases.

DOI PMID

[22]
邓亚娟,杨云峰,马荣国.基于复杂网络理论的公路网结构特征[J].中国公路学报,2010,23(1):98-104.为进一步分析复杂公路网中线路的重要程度,采用对偶拓扑方法,将公路路段按照路名抽象为节点,将交叉口抽象为网络边,对实际公路网进行拓扑结构转换;通过构建网络可靠性指标,应用复杂网络节点度、接近中心性、中介中心性以及连通可靠性指标评价区域公路网结构特征,并给出基于模糊聚类的公路网等级划分方法。分析结果表明:基于对偶拓扑方法,应用复杂网络理论进行公路网结构特征研究,可从连通性、中心性、中间性和可靠性等多个角度反映线路在公路网中的重要程度。

[ Deng Y J, Yang Y F, Ma R G.The structure characteristics of highway network based on complex network theory[J]. China Journal of Highway & Transport, 2010,23(1):98-104. ]

Options
文章导航

/

〈 〉