Traffic congestion in interconnected complex networks

Global efficiency and network structure of urban traffic flows: A percolation-based empirical analysis

Making the connection between the function and structure of networked systems is one of the fundamental issues in complex systems and network science. Urban traffic flows are related to various problems in cities and can be represented as a network of local traffic flows. To identify an empirical relation between the function and network structure of urban traffic flows, we construct a time-varying traffic flow network of a megacity, Seoul, and analyze its global efficiency with a percolation-based approach. Comparing the real-world traffic flow network with its corresponding null-model network having a randomized structure, we show that the real-world network is less efficient than its null-model network during rush hour, yet more efficient during non-rush hour. We observe that in the real-world network, links with the highest betweenness tend to have lower quality during rush hour compared to links with lower betweenness, but higher quality during non-rush hour. Since the top betweenness links tend to be the bridges that connect the network together, their congestion has a stronger impact on the network's global efficiency. Our results suggest that the spatial structure of traffic flow networks is important to understand their function.

Efficient routing for spatial networks

In many complex networks, the main task is to transfer load from sources to destinations. Therefore, the network throughput is a very important indicator to measure the network performance. In order to improve the network throughput, researchers have proposed many effective routing strategies. Spatial networks, as a class of complex networks, exist widely in the real-world. However, the existing routing strategies in complex networks cannot achieve good results when applied in spatial networks. Therefore, in this paper, we propose a new degree-location ( D L) routing strategy to improve the throughput of spatial networks. In this routing strategy, the load transmitted from sources to destinations will bypass the nodes with high degrees and the nodes located close to the center of region. Simulations on homogeneous and heterogeneous spatial networks show that the D L routing strategy proposed in this paper can effectively improve the throughput of the network. The result of this paper can help the routing design of spatial networks and may find applications in many real-world spatial networks to improve the transmission performance.

Traffic-driven epidemic spreading in multiplex networks

Recent progress on multiplex networks has provided a powerful way to abstract the diverse interaction of a network system with multiple layers. In this paper, we show that a multiplex structure can greatly affect the spread of an epidemic driven by traffic dynamics. One of the interesting findings is that the multiplex structure could suppress the outbreak of an epidemic, which is different from the typical finding of spread dynamics in multiplex networks. In particular, one layer with dense connections can attract more traffic flow and eventually suppress the epidemic outbreak in other layers. Therefore, the epidemic threshold will be larger than the minimal threshold of the layers. With a mean-field approximation, we provide explicit expressions for the epidemic threshold and for the onset of suppressing epidemic spreading in multiplex networks. We also provide the probability of obtaining a multiplex configuration that suppresses the epidemic spreading when the multiplex is composed of: (i) two Erdős-Rényi layers and (ii) two scale-free layers. Therefore, compared to the situation of an isolated network in which a disease may be able to propagate, a larger epidemic threshold can be found in multiplex structures.

Effective traffic-flow assignment strategy on multilayer networks

An efficient flow assignment strategy is of great importance to alleviate traffic congestion on multilayer networks. In this work, by considering the roles of nodes' local structures on the microlevel, and the different transporting speeds of layers in the macrolevel, an effective traffic-flow assignment strategy on multilayer networks is proposed. Both numerical and semianalytical results indicate that our proposed flow assignment strategy can reasonably redistribute the traffic flow of the low-speed layer to the high-speed layer. In particular, preferentially transporting the packets through small-degree nodes on the high-speed layer can enhance the traffic capacity of multilayer networks. We also find that the traffic capacity of multilayer networks can be improved by increasing the network size and the average degree of the high-speed layer. For a given multilayer network, there is a combination of optimal macrolevel parameter and optimal microlevel parameter with which the traffic capacity can be maximized. It is verified that real-world network topology does not invalidate the results. The semianalytical predictions agree with the numerical simulations.

Influence of Different Coupling Modes on the Robustness of Smart Grid under Targeted Attack

Many previous works only focused on the cascading failure of global coupling of one-to-one structures in interdependent networks, but the local coupling of dual coupling structures has rarely been studied due to its complex structure. This will result in a serious consequence that many conclusions of the one-to-one structure may be incorrect in the dual coupling network and do not apply to the smart grid. Therefore, it is very necessary to subdivide the dual coupling link into a top-down coupling link and a bottom-up coupling link in order to study their influence on network robustness by combining with different coupling modes. Additionally, the power flow of the power grid can cause the load of a failed node to be allocated to its neighboring nodes and trigger a new round of load distribution when the load of these nodes exceeds their capacity. This means that the robustness of smart grids may be affected by four factors, i.e., load redistribution, local coupling, dual coupling link and coupling mode; however, the research on the influence of those factors on the network robustness is missing. In this paper, firstly, we construct the smart grid as a two-layer network with a dual coupling link and divide the power grid and communication network into many subnets based on the geographical location of their nodes. Secondly, we define node importance (NI) as an evaluation index to access the impact of nodes on the cyber or physical network and propose three types of coupling modes based on NI of nodes in the cyber and physical subnets, i.e., Assortative Coupling in Subnets (ACIS), Disassortative Coupling in Subnets (DCIS), and Random Coupling in Subnets (RCIS). Thirdly, a cascading failure model is proposed for studying the effect of local coupling of dual coupling link in combination with ACIS, DCIS, and RCIS on the robustness of the smart grid against a targeted attack, and the survival rate of functional nodes is used to assess the robustness of the smart grid. Finally, we use the IEEE 118-Bus System and the Italian High-Voltage Electrical Transmission Network to verify our model and obtain the same conclusions: (I) DCIS applied to the top-down coupling link is better able to enhance the robustness of the smart grid against a targeted attack than RCIS or ACIS, (II) ACIS applied to a bottom-up coupling link is better able to enhance the robustness of the smart grid against a targeted attack than RCIS or DCIS, and (III) the robustness of the smart grid can be improved by increasing the tolerance α. This paper provides some guidelines for slowing down the speed of the cascading failures in the design of architecture and optimization of interdependent networks, such as a top-down link with DCIS, a bottom-up link with ACIS, and an increased tolerance α.

Network recovery based on system crash early warning in a cascading failure model

This paper investigates the possibility of saving a network that is predicted to have a cascading failure that will eventually lead to a total collapse. We model cascading failures using the recently proposed KQ model. Then predict an impending total collapse by monitoring critical slowing down indicators and subsequently attempt to prevent the total collapse of the network by adding new nodes. To this end, we systematically evaluate five node addition rules, the effect of intervention delay and network degree heterogeneity. Surprisingly, unlike for random homogeneous networks, we find that a delayed intervention is preferred for saving scale free networks. We also find that for homogeneous networks, the best strategy is to wire newly added nodes to existing nodes in a uniformly random manner. For heterogeneous networks, however, a random selection of nodes based on their degree mostly outperforms a uniform random selection. These results provide new insights into restoring networks by adding nodes after observing early warnings of an impending complete breakdown.

Traffic congestion and the lifetime of networks with moving nodes

For many power-limited networks, such as wireless sensor networks and mobile ad hoc networks, maximizing the network lifetime is the first concern in the related designing and maintaining activities. We study the network lifetime from the perspective of network science. In our model, nodes are initially assigned a fixed amount of energy moving in a square area and consume the energy when delivering packets. We obtain four different traffic regimes: no, slow, fast, and absolute congestion regimes, which are basically dependent on the packet generation rate. We derive the network lifetime by considering the specific regime of the traffic flow. We find that traffic congestion inversely affects network lifetime in the sense that high traffic congestion results in short network lifetime. We also discuss the impacts of factors such as communication radius, node moving speed, routing strategy, etc., on network lifetime and traffic congestion.

Transportation dynamics on coupled networks with limited bandwidth

The communication networks in real world often couple with each other to save costs, which results in any network does not have a stand-alone function and efficiency. To investigate this, in this paper we propose a transportation model on two coupled networks with bandwidth sharing. We find that the free-flow state and the congestion state can coexist in the two coupled networks, and the free-flow path and congestion path can coexist in each network. Considering three bandwidth-sharing mechanisms, random, assortative and disassortative couplings, we also find that the transportation capacity of the network only depends on the coupling mechanism, and the fraction of coupled links only affects the performance of the system in the congestion state, such as the traveling time. In addition, with assortative coupling, the transportation capacity of the system will decrease significantly. However, the disassortative coupling has little influence on the transportation capacity of the system, which provides a good strategy to save bandwidth. Furthermore, a theoretical method is developed to obtain the bandwidth usage of each link, based on which we can obtain the congestion transition point exactly.

Impact of Degree Heterogeneity on Attack Vulnerability of Interdependent Networks

The study of interdependent networks has become a new research focus in recent years. We focus on one fundamental property of interdependent networks: vulnerability. Previous studies mainly focused on the impact of topological properties upon interdependent networks under random attacks, the effect of degree heterogeneity on structural vulnerability of interdependent networks under intentional attacks, however, is still unexplored. In order to deeply understand the role of degree distribution and in particular degree heterogeneity, we construct an interdependent system model which consists of two networks whose extent of degree heterogeneity can be controlled simultaneously by a tuning parameter. Meanwhile, a new quantity, which can better measure the performance of interdependent networks after attack, is proposed. Numerical simulation results demonstrate that degree heterogeneity can significantly increase the vulnerability of both single and interdependent networks. Moreover, it is found that interdependent links between two networks make the entire system much more fragile to attacks. Enhancing coupling strength between networks can greatly increase the fragility of both networks against targeted attacks, which is most evident under the case of max-max assortative coupling. Current results can help to deepen the understanding of structural complexity of complex real-world systems.

Congestion Induced by the Structure of Multiplex Networks

Multiplex networks are representations of multilayer interconnected complex networks where the nodes are the same at every layer. They turn out to be good abstractions of the intricate connectivity of multimodal transportation networks, among other types of complex systems. One of the most important critical phenomena arising in such networks is the emergence of congestion in transportation flows. Here, we prove analytically that the structure of multiplex networks can induce congestion for flows that otherwise would be decongested if the individual layers were not interconnected. We provide explicit equations for the onset of congestion and approximations that allow us to compute this onset from individual descriptors of the individual layers. The observed cooperative phenomenon is reminiscent of Braess' paradox in which adding extra capacity to a network when the moving entities selfishly choose their route can in some cases reduce overall performance. Similarly, in the multiplex structure, the efficiency in transportation can unbalance the transportation loads resulting in unexpected congestion.

Physics of transportation: Towards optimal capacity using the multilayer network framework

Because of the critical role of transportation in modern times, one of the most successful application areas of statistical physics of complex networks is the study of traffic dynamics. However, the vast majority of works treat transportation networks as an isolated system, which is inconsistent with the fact that many complex networks are interrelated in a nontrivial way. To mimic a realistic scenario, we use the framework of multilayer networks to construct a two-layered traffic model, whereby the upper layer provides higher transport speed than the lower layer. Moreover, passengers are guided to travel along the path of minimal travelling time and with the additional cost they can transfer from one layer to another to avoid congestion and/or reach the final destination faster. By means of numerical simulations, we show that a degree distribution-based strategy, although facilitating the cooperation between both layers, can be further improved by enhancing the critical generating rate of passengers using a particle swarm optimisation (PSO) algorithm. If initialised with the prior knowledge from the degree distribution-based strategy, the PSO algorithm converges considerably faster. Our work exemplifies how statistical physics of complex networks can positively affect daily life.

Integrated travel network model for studying epidemics: Interplay between journeys and epidemic

The ease of travelling between cities has contributed much to globalization. Yet, it poses a threat on epidemic outbreaks. It is of great importance for network science and health control to understand the impact of frequent journeys on epidemics. We stress that a new framework of modelling that takes a traveller's viewpoint is needed. Such integrated travel network (ITN) model should incorporate the diversity among links as dictated by the distances between cities and different speeds of different modes of transportation, diversity among nodes as dictated by the population and the ease of travelling due to infrastructures and economic development of a city, and round-trip journeys to targeted destinations via the paths of shortest travel times typical of human journeys. An example is constructed for 116 cities in China with populations over one million that are connected by high-speed train services and highways. Epidemic spread on the constructed network is studied. It is revealed both numerically and theoretically that the traveling speed and frequency are important factors of epidemic spreading. Depending on the infection rate, increasing the traveling speed would result in either an enhanced or suppressed epidemic, while increasing the traveling frequency enhances the epidemic spreading.

Robust-yet-fragile nature of interdependent networks

Interdependent networks have been shown to be extremely vulnerable based on the percolation model. Parshani et al. [Europhys. Lett. 92, 68002 (2010)] further indicated that the more intersimilar networks are, the more robust they are to random failures. When traffic load is considered, how do the coupling patterns impact cascading failures in interdependent networks? This question has been largely unexplored until now. In this paper, we address this question by investigating the robustness of interdependent Erdös-Rényi random graphs and Barabási-Albert scale-free networks under either random failures or intentional attacks. It is found that interdependent Erdös-Rényi random graphs are robust yet fragile under either random failures or intentional attacks. Interdependent Barabási-Albert scale-free networks, however, are only robust yet fragile under random failures but fragile under intentional attacks. We further analyze the interdependent communication network and power grid and achieve similar results. These results advance our understanding of how interdependency shapes network robustness.