Deterministic weighted scale-free small-world networks

We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the co-evolution of topology and weight. Considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks, we suggest a recursive algorithm to generate the network, which restricts the traffic fluctuations on it effectively during the evolutionary process. We provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution, degree correlations, average clustering coefficient and degree-cluster correlations as well as the diameter.     

Congestion analysis of traffic networks with direction-dependant heterogeneity

Traffic flow directionality and network weight asymmetry are widespread notions in traffic networks. This paper investigates the influence of direction-dependant heterogeneity on traffic congestion. To capture the effect of the link directionality and link weight asymmetry, the heterogeneity indexes of complex networks and the traffic flow model are introduced. The numerical results show that the critical value of heterogeneity determines congestion transition processes. The congestion degree increases with heterogeneity when the network heterogeneity is at a subcritical region. A network is more tolerant of congestion if the heterogeneity of the network is smaller or larger than the critical value. Furthermore, when heterogeneity reaches the critical value, the average number of accumulated vehicles arrives at the maximum and the traffic flow is under a serious congestion state. A significant improvement on the tolerance to congestion of traffic networks can be made if the network heterogeneity is controlled within a reasonable range.     

Optimal structure of complex networks for minimizing traffic congestion

To design complex networks to minimize traffic congestion, it is necessary to understand how traffic flow depends on network structure. We study data packet flow on complex networks, where the packet delivery capacity of each node is not fixed. The optimal configuration of capacities to minimize traffic congestion is derived and the critical packet generating rate is determined, below which the network is at a free flow state but above which congestion occurs. Our analysis reveals a direct relation between network topology and traffic flow. Optimal network structure, free of traffic congestion, should have two features: uniform distribution of load over all nodes and small network diameter. This finding is confirmed by numerical simulations. Our analysis also makes it possible to theoretically compare the congestion conditions for different types of complex networks. In particular, we find that network with low critical generating rate is more susceptible to congestion. The comparison has been made on the following complex-network topologies: random, scale-free, and regular.     

复杂交通运输网络上的拥挤与效率问题研究

本文研究复杂交通运输网络上的拥挤与效率问题. 在无标度网络、随机网络以及小世界网络等不同拓扑结构中, 探讨了不同的能力分配方式和不同的OD (Origin-Destination) 交通需求分布对网络拥挤度和效率的影响. 随着平均交通需求的增加, 分析无标度网络、随机网络以及小世界网络从自由流状态到交通拥堵状态的变化规律. 为便于比较, 本文侧重研究网络拥挤度的倒数, 并将其定义为通畅度. 研究发现网络中的通畅度与效率之间存在线性相关关系, 并且不同网络中的线性比例系数 (或斜率)是不同的, 从而体现了不同网络具有不同的运输性能. 关键词： 复杂网络 拥挤 效率     

结合可视图的多状态交通流时间序列特性分析

交通流时间序列的研究主要采用数据挖掘和机器学习的方法,这些"黑箱"挖掘方法很难直观反映序列特性.为增强交通流时间序列及其特征分析的可视化性,结合可视图理论来构建交通流时间序列的关联网络,从复杂网络角度实现交通流时间序列的特性分析.在网络构建的过程中,考虑到不同交通状态下交通流表征具有的差异性,首先利用交通流参量的相关性对交通流状态进行分类,然后构建不同交通状态下的时间序列复杂网络,并对这些网络的特征属性给出统计分析,如度分布、聚类系数、网络直径、模块化等.研究表明,可视图法可为交通流时间序列映射到网络提供有效途径,并且不同状态下交通流时间序列构建的复杂网络的模块化、聚类系数和度分布等统计特征呈现一定的变化规律,为交通流运行态势的研究提供了可视化的分析角度.     

Traffic of indistinguishable particles in complex networks

In this paper, we apply a simple walk mechanism to the study of the traffic of many indistinguishable particles in complex networks. The network with particles stands for a particle system, and every vertex in the network stands for a quantum state with the corresponding energy determined by the vertex degree. Although the particles are indistinguishable, the quantum states can be distinguished. When the many indistinguishable particles walk randomly in the system for a long enough time and the system reaches dynamic equilibrium, we find that under different restrictive conditions the particle distributions satisfy different forms, including the Bose--Einstein distribution, the Fermi--Dirac distribution and the non-Fermi distribution (as we temporarily call it). As for the Bose--Einstein distribution, we find that only if the particle density is larger than zero, with increasing particle density, do more and more particles condense in the lowest energy level. While the particle density is very low, the particle distribution transforms from the quantum statistical form to the classically statistical form, i.e., transforms from the Bose distribution or the Fermi distribution to the Boltzmann distribution. The numerical results fit well with the analytical predictions.     

Characterizing traffic time series based on complex network theory

A complex network is a powerful tool to research complex systems, traffic flow being one of the most complex systems. In this paper, we use complex network theory to study traffic time series, which provide a new insight into traffic flow analysis. Firstly, the phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem. Secondly, in order to convert the new time series into a complex network, the critical threshold is estimated by the characteristics of a complex network, which include degree distribution, cumulative degree distribution, and density and clustering coefficients. We find that the degree distribution of associated complex network can be fitted with a Gaussian function, and the cumulative degree distribution can be fitted with an exponential function. Density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network, and the results are in accordance with the observation of the plot of an adjacent matrix. Consequently, based on complex network analysis, the proper range of the critical threshold is determined. Finally, to mine the nodes with the closest relations in a complex network, the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity. The work in our paper provides a new way to understand the dynamics of traffic time series.     

无标度复杂网络负载传输优化策略

提出了一种能够显著提高无标度复杂网络负载传输性能的优化路由策略.实现了负载在核心节点与边缘节点间的合理分配.分析表明该策略使得网络的负载处理能力正比于网络规模的平方,而与单个节点的度值无关.实验结果显示优化路由策略在保持了最短路由策略小世界效应的同时,成倍地提升了网络的负载传输能力,且随着网络平均节点度的增加其优势越趋显著.此外,与有效路由策略的比较进一步验证了优化路由策略的优异性能. 关键词： 优化路由策略 复杂网络 负载传输 网络阻塞     

Research on the search ability of Brownian particles on networks with an adaptive mechanism

In this paper, we focus on the search ability of Brownian particles with an adaptive mechanism. In the adaptive mechanism, nodes are allowed to be able to change their own accepting probability according to their congestion states. Two searching-traffic models, the static one in which nodes have fixed accepting probability to the incoming particles and the adaptive one in which nodes have adaptive accepting probability to the incoming particles are presented for testing the adaptive mechanism. Instead of number of hops, we use the traveling time, which includes not only the number of hops for a particle to jump from the source node to the destination but also the time that the particle stays in the queues of nodes, to evaluate the search ability of Brownian particles. We apply two models to different networks. The experiment results show that the adaptive mechanism can decrease the network congestion and the traveling time of the first arriving particle. Furthermore, we investigate the influence of network topologies on the congestion of networks by addressing several main properties: degree distribution, average path length, and clustering coefficient. We show the reason why random topologies are more able to deal with congested traffic states than others. We also propose an absorption strategy to deal with the additional Brownian particles in networks. The experiment results on Barabási–Albert (BA) scale-free networks show that the absorption strategy can increase the probability of a successful search and decrease the average per-node particles overhead for our models.     

基于感知流量算法的复杂网络拥塞问题研究

研究了在具有感知流量的路由策略下,复杂网络的拓扑结构对网络中传输流量的影响.为了描述数据包传输过程的有效性,通过引入一个状态参数,利用由稳态到拥塞的指标流量相变值来刻画网络的吞吐量.基于每个节点的数据包处理能力与该节点的度或介数成比例提出两种模型并进行仿真.仿真结果表明,平均度相同的情况下,模型Ⅰ中,WS小世界网络比ER随机网络和BA无标度网络更容易产生拥塞;模型Ⅱ中,所有网络容量都得到较大的提高,尤其是WS小世界网络.但当网络的基本连接参数改变时,哪种模型更利于网络的流量传输,还要依据网络本身的结构特性 关键词： 复杂网络 无标度网络 感知流量 拥塞     

无标度网络上队列资源分配研究

研究了节点队列资源有限的条件下,无标度网络上的信息流动力学过程,发现了网络由自由流通到拥塞的相变现象,提出了一种基于节点度的队列资源分配模型.模型的核心是使节点i的队列长度与kβi成正比(ki为节点i的度,β为分配参数).仿真结果表明,在网络使用最短路径算法进行信息包传送的条件下,β近似等于1.25时队列资源分配最合理,网络容量最大,且该最佳值与队列总资源多少以及网络的规模无关.     

Effects of the cascading failures on scale-free traffic networks

In this paper, we consider the artificial scale-free traffic network with dynamic weights (cost) and focus on how the removal strategies (flow-based removal, betweenness-based removal and mix-based removal) affect the damage of cascading failures based on the user-equilibrium (UE) assignment, which ensures the balance of flow on the traffic network. Experiment simulation shows that different removal strategies can bring large dissimilarities of the efficiency and damage after the intentional removal of an edge. We show that the mix-based removal of a single edge might reduce the damage of cascading failures and delay the breakdown time, especially for larger reserve capacity coefficient α. This is particularly important for real-world networks with a highly hetereogeneous distribution of flow, i.e., traffic and transportation networks, logistics networks and electrical power grids.     

Traffic dynamics based on a traffic awareness routing strategy on scale-free networks

By incorporating local traffic information into the shortest path routing strategy, we numerically investigate the effectiveness of the traffic awareness routing strategy for scale-free networks with different clustering. In order to characterize the efficiency of the packet-delivery process, we introduce an order parameter and an average transmission time that allow us to measure the network capacity by the critical value of phase transition from free flow to congestion. Compared with the shortest path routing protocol, the network capacity is greatly enhanced by the traffic awareness routing strategy. We also find that there exists an optimum value for the tunable parameter in the congestion awareness strategy. Moreover, simulation results show that the more clustered the network, the less efficient the packet-delivery process.     

Routing in scale-free networks based on expanding betweenness centrality

In this paper, an improved routing strategy is proposed for enhancing the traffic capacity of scale-free networks. Instead of using the information of degree and betweenness centrality, the new algorithm is derived on the basis of the expanding betweenness centrality of nodes, which gives an estimate of the traffic handled by the vertex for a certain route set. Since the nodes with large betweenness centrality are more susceptible to traffic congestion, the traffic can be improved by redistributing traffic loads from nodes with large betweenness centrality to nodes with small betweenness centrality in the process of computing the collective routing table. Comparing with results of previous routing strategies, it is shown that the present improved routing performs more effectively.     

Traffic dynamics on layered complex networks

To minimize traffic congestion, understanding how traffic dynamics depend on network structure is necessary. Many real-world complex systems can be described as multilayer structures. In this paper, we introduce the idea of layers to establish a traffic model of two-layer complex networks. By comparing different two-layer complex networks based on random and scale-free networks, we find that the physical layer is much more important to the network capacity of two-layer complex networks than the logical layer. Two-layer complex networks with a homogeneous physical topology are found to be more tolerant to congestion. Moreover, simulation results show that the heterogeneity of logical and physical topologies makes the packet-delivery process of two-layer networks more efficient in the free-flow state, without the occurrence of traffic congestion.     

Road traffic: A case study of flow and path-dependency in weighted directed networks

How much can we tell about flows through networks just from their topological properties? Whereas flow distributions of river basins, trees or cardiovascular systems come naturally to mind, more complex topologies are not so immediate, especially if the network is large and heterogeneously directed. Our study is motivated by the question of how the distribution of path-dependent trails in directed networks is correlated to the distribution of network flows. As an example we have studied the path-dependencies in closed trails in four metropolitan areas in England and the USA and computed their global and spatial correlations with measured traffic flows. We have found that the heterogeneous distribution of traffic intensity is mirrored by the distribution of agglomerate path-dependency and that high traffic roads are packed along corridors at short-to-medium trail lengths from the ensemble of nodes.     

Dynamics of traffic networks: From microscopic and macroscopic perspectives

Considering the microscopic characteristics (vehicle speed, road length etc.) of links and macroscopic behaviors of traffic systems, we derive the critical flow generation rate in scale-free networks. And the dynamics of traffic congestion is studied numerically in this paper. It is shown that the queue length increases with microscopic characteristics of links. Additionally, the critical flow generation rate decreases with increase of the network size N, maximum speed v_max and parameter τ. The significance of this finding is that, in order to improve the traffic environment, both the local information for the single link and behaviors of the whole network must be analyzed simultaneously in a traffic system design.     

Empirical topological investigation of practical supply chains based on complex networks

The industrial supply chain networks basically capture the circulation of social resource, dominating the stability and efficiency of the industrial system. In this paper, we provide an empirical study of the topology of smartphone supply chain network. The supply chain network is constructed using open online data. Our experimental results show that the smartphone supply chain network has small-world feature with scale-free degree distribution, in which a few high degree nodes play a key role in the function and can effectively reduce the communication cost. We also detect the community structure to find the basic functional unit. It shows that information communication between nodes is crucial to improve the resource utilization. We should pay attention to the global resource configuration for such electronic production management.     

Optimization in gradient networks

Gradient networks can be used to model the dominant structure of complex networks. Previous work has focused on random gradient networks. Here we study gradient networks that minimize jamming on substrate networks with scale-free and Erdos-Renyi structure. We introduce structural correlations and strongly reduce congestion occurring on the network by using a Monte Carlo optimization scheme. This optimization alters the degree distribution and other structural properties of the resulting gradient networks. These results are expected to be relevant for transport and other dynamical processes in real network systems.