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Conventional resource allocation strategies, such as the Simplest Average (SA) resource allocation strategy, often assume identical transmission capacity for all nodes, failing to account for the actual importance of nodes within the network, especially in three-layer networks where inadequate resource allocation to hub nodes can significantly impact performance. Existing methods are primarily designed for single-layer networks and struggle to address the complexity and interdependencies of real-world multi-layer structures, thus limiting the optimization of network traffic capacity. This paper proposes an Effective Logarithm-Degree (EL) resource allocation strategy that allocates node delivery capacity based on the ratio of the logarithmic degrees of nodes across the logical and physical layers. Compared to the Simplest Average resource allocation strategy, the Effective Logarithm-Degree strategy significantly enhances network traffic capacity, increasing it by over 1.4 times and reducing traffic load by 60%, while also optimizing the load balance. Simulation results validate the superiority of the Effective Logarithm-Degree strategy in improving performance and resource utilization efficiency in three-layer network environments.

Since the betweenness of nodes in complex networks can theoretically represent the traffic load of nodes under the currently used routing strategy, we propose an improved efficient (IE) routing strategy to enhance to the network traffic capacity based on the betweenness centrality. Any node with the highest betweenness is susceptible to traffic congestion. An efficient way to improve the network traffic capacity is to redistribute the heavy traffic load from these central nodes to non-central nodes, so in this paper, we firstly give a path cost function by considering the sum of node betweenness with a tunable parameter β along the actual path. Then, by minimizing the path cost, our IE routing strategy achieved obvious improvement on the network transport efficiency. Simulations on scale-free Barabási–Albert (BA) networks confirmed the effectiveness of our strategy, when compared with the efficient routing (ER) and the shortest path (SP) routing.

Traffic capacity is critical for various networks and strongly depends on the distribution of link's bandwidth resources. In this paper, we propose a betweenness-based bandwidth allocation strategy in which the bandwidth of each link l_ij is allocated proportionally to the product (1 + B_i)^α(1 + B_j)^α, where α is a tunable parameter, and B_i and B_j are the betweenness of node i and node j, respectively. The optimal value of α is achieved by extensive simulations and slightly increases with the network size. Our new bandwidth allocation strategy achieves the highest traffic capacity when compared with the average bandwidth allocation strategy and the previously proposed degree-based bandwidth allocation strategy. Our work will be beneficial for network service providers to improve the traffic capacity by efficiently allocating or reallocating the overall finite link's bandwidth resources of networks such as the Internet, urban transport networks and airway networks.

In real communication systems, each node has a finite queue length to store packets due to physical constraints. In this paper, we propose a queue resource allocation strategy for traffic dynamics in scale-free networks. With a finite resource of queue, the allocation of queue length on node i is based on B_i, where B_i is the generalized betweenness centrality of node i. The overall traffic capacity of a network system can be evaluated by the critical packet generating rate (R_c). Through the use of the proposed queue allocation scheme for the shortest path protocol and efficient routing protocol, our strategy performs better than the uniform queue length allocation strategy, which is demonstrated by a larger value of the critical generating rate. We also give a method to estimate the network traffic capacity theoretically.

As two-layer or multi-layer network model can more accurately reveal many real structures of complex systems such as peer-to-peer (P2P) networks on IP networks, to better understand the traffic dynamics and improve the network traffic capacity, we propose to efficiently construct the structure of upper logical layer network which can be possibly implemented. From the beginning, we assume that the logical layer network has the same structure as the lower physical layer network, and then we use link-removal strategy in which a fraction of links with maximal product (k_i* k_j) are removed from the logical layer, where k_i and k_j are the degrees of node i and node j, respectively. Traffic load is strongly redistributed from center nodes to noncenter nodes. The traffic capacity of whole complex system is enhanced several times at the expense of a little average path lengthening. In two-layer network model, the physical layer network structure is unchanged and the shortest path routing strategy is used. The structure of upper layer network can been constructed freely under our own methods. This mechanism can be employed in many real complex systems to improve the network traffic capacity.

In this paper, we propose an efficient strategy to enhance the network transport efficiency by adding links to the existing networks. In our proposed strategy, we consider both the node betweenness centrality (BC) and the shortest path length (L) as two important factors. The overall traffic capacity of a network system can be evaluated by the critical packet generating rate R_c. Simulation results show that the proposed strategy can bring better traffic capacity and shorter average shortest path length than the low-degree-first (LDF) strategy and the low-betweenness-first (LBF) strategy. This work is helpful for designing and optimizing of realistic networks.

Provided that node delivery capacity may be not uniformly distributed in many realistic networks, we present a node delivery capacity distribution in which each node capacity is composed of uniform fraction and degree related proportion. Based on the node delivery capacity distribution, we construct a novel routing mechanism called efficient weighted routing (EWR) strategy to enhance network traffic capacity and transportation efficiency. Compared with the shortest path routing and the efficient routing strategies, the EWR achieves the highest traffic capacity. After investigating average path length, network diameter, maximum efficient betweenness, average efficient betweenness, average travel time and average traffic load under extensive simulations, it indicates that the EWR appears to be a very effective routing method. The idea of this routing mechanism gives us a good insight into network science research. The practical use of this work is prospective in some real complex systems such as the Internet.

The transport efficiency of a network is strongly related to the underlying structure. In this paper, we propose an efficient strategy named high-betweenness-first (HBF) for the purpose of improving the traffic handling capacity of scale-free networks by limiting a fraction of undirected links to be unidirectional ones based on the links’ betweenness. Compared with the high-degree-first (HDF) strategy, the traffic capacity can be more significantly enhanced under the proposed link-directed strategy with the shortest path (SP) routing protocol. Simulation results in the Barabási–Albert (BA) model for scale-free networks show that the critical generating rate $R_c$ which can evaluate the overall traffic capacity of a network system is larger after applying the HBF strategy, especially with nonrandom direction-determining rules. Because of the strongly improved traffic capacity, this work is helpful to design and optimize modern communication networks such as the software defined network.

The traffic dynamics of multi-layer networks has become a hot research topic since many networks are comprised of two or more layers of subnetworks. Due to its low traffic capacity, the traditional shortest path routing (SPR) protocol is susceptible to congestion on two-layer complex networks. In this paper, we propose an efficient routing strategy named improved global awareness routing (IGAR) strategy which is based on the betweenness centrality of nodes in the two layers. With the proposed strategy, the routing paths can bypass hub nodes of both layers to enhance the transport efficiency. Simulation results show that the IGAR strategy can bring much better traffic capacity than the SPR and the global awareness routing (GAR) strategies. Because of the significantly improved traffic performance, this study is helpful to alleviate congestion of the two-layer complex networks.

The transport efficiency is one of the critical parameters to evaluate the performance of a network. In this paper, we propose an improved efficient (IE) strategy to enhance the network transport efficiency of complex networks by adding a fraction of links to an existing network based on the node’s local degree centrality and the shortest path length. Simulation results show that the proposed strategy can bring better traffic capacity and shorter average shortest path length than the low-degree-first (LDF) strategy under the shortest path routing protocol. It is found that the proposed strategy is beneficial to the improvement of overall traffic handling and delivering ability of the network. This study can alleviate the congestion in networks, and is helpful to design and optimize realistic networks.

Existing routing strategies such as the global dynamic routing [X. Ling, M. B. Hu, R. Jiang and Q. S. Wu, Phys. Rev. E81, 016113 (2010)] can achieve very high traffic capacity at the cost of extremely long packet traveling delay. In many real complex networks, especially for real-time applications such as the instant communication software, extremely long packet traveling time is unacceptable. In this work, we propose to assign a finite Time-to-Live (TTL) parameter for each packet. To guarantee every packet to arrive at its destination within its TTL, we assume that a packet is retransmitted by its source once its TTL expires. We employ source routing mechanisms in the traffic model to avoid the routing-flaps induced by the global dynamic routing. We compose extensive simulations to verify our proposed mechanisms. With small TTL, the effects of packet retransmission on network traffic capacity are obvious, and the phase transition from flow free state to congested state occurs. For the purpose of reducing the computation frequency of the routing table, we employ a computing cycle $T_c$ within which the routing table is recomputed once. The simulation results show that the traffic capacity decreases with increasing $T_c$. Our work provides a good insight into the understanding of effects of packet retransmission with finite packet lifetime on traffic capacity in scale-free networks.

Traffic is one of the most fundamental dynamical processes in networked systems. With the traditional shortest path routing (SPR) protocol, traffic congestion is likely to occur on the hub nodes on scale-free networks. In this paper, we propose an improved optimal routing (IOR) strategy which is based on the betweenness centrality and the degree centrality of nodes in the scale-free networks. With the proposed strategy, the routing paths can accurately bypass hub nodes in the network to enhance the transport efficiency. Simulation results show that the traffic capacity as well as some other indexes reflecting transportation efficiency are further improved with the IOR strategy. Owing to the significantly improved traffic performance, this study is helpful to design more efficient routing strategies in communication or transportation systems.

The traffic dynamics of complex networks are largely determined by the node’s resource distribution. In this paper, based on the shortest path routing strategy, a node delivering capacity distribution mechanism is proposed into the traffic dynamics in Barabási and Albert (BA) scale-free networks; the efficiency of the mechanism on the network capacity measured by the critical point ($R_c$) of phase transition from free flow to congestion is primarily explored. Based on the proposed strategy, the total delivering capacity is reallocated according to both degree and betweenness of each node, and an optimal value of parameter ${\alpha }_c$ is found, leading to the maximum traffic capacity. The results of numerical experiments on scale-free networks suggest that the resource allocation strategy proposed here is capable of effectively enhancing the transmission capacity of networks. Furthermore, this study may provide novel insights into research on networked traffic systems.

The network topology structure has great impact on its traffic capacity. Most of the biological and technological networks have been proved to exhibit scale-free feature. In real networks, the hub links, which usually bear large traffic loads, have restricted transport efficiency of the complex networks. In this paper, we focus on the bandwidth congestion and propose a rewiring link strategy to optimize traffic dynamics on scale-free networks. Two link rewiring strategies are compared and the simulation results on scale-free networks show that our strategy has more advantages, which makes the degree distribution of the network more uniform, reducing the average path length of different nodes, balancing the resources of the network and increasing the traffic capacity of the network. This work will be beneficial for designing network topology and optimizing network performances.

In complex networks, how topology structures influence the traffic dynamics on networks is a hot topic. The existence of structure within communities may affect the transmission of data packets in the network. In this paper, we investigate the impact of community structure on traffic dynamics in random networks which are homogeneous. It is found that three key factors influence traffic capacity in such community networks: community number, community strength, and average node degree. The increase of average node degree increases traffic capacity, while the increase of community number and community strength decreases traffic capacity.

In this paper, we propose a Structural Hole Routing (SHR) strategy based on the structural hole theory for scale-free networks. The performance of routing strategies on scale-free networks can be measured by two indicators, i.e. the traffic capacity and the average path length. With the SHR strategy, the packets can bypass those center nodes to enhance the traffic capacity of scale-free networks. The simulation results show that our SHR strategy can achieve approximately 6% higher traffic capacity than the efficient routing (ER) strategy. Moreover, the average path length of the SHR strategy is a little higher than that of the ER strategy. Therefore, our SHR routing strategy is preferable to other routing strategies and can be easily implemented through software method.

To improve the traffic capacity of scale-free networks, we propose an improved local efficient routing (ILER) strategy based on node degree and network constraint index (NCI). NCI describes how closely a node is maintained directly or indirectly with other nodes, and it only considers the relationship between nodes and their neighbors, not the topology of the network. Both the node degree and NCI are a parameter to describe the importance of nodes, and the combination of the two can make up for their own shortcomings, making it particularly important. Under the ILER strategy, packets can bypass some central nodes in the network for transmission, so that the central nodes in the network are not prone to congestion, thereby increasing the network traffic capacity. Through simulation comparison, the network traffic capacity under ILER strategy is significantly higher than that under probability routing (PR) strategy and efficient routing (ER) strategy. Under the ILER strategy, the average path length (APL) of the network is also shorter than that under the PR and ER strategies. In addition, whether target attack or random attack, the network has strong robustness under ILER strategy.

The network structure acquires great influence on the traffic capacity for complex network. Since the nodes with high degree usually bear large load in the process of packet transmission, we propose a new multilayer network model which can balance the load of low-speed and high-speed layers. The simulation results show that compared with the randomly select nodes multilayer network model, the new network model makes the multilayer network load more balanced, thereby enhancing traffic capacity of the network and reducing the possibility of congestion. This network model gives full play to the transmission advantages of the high-speed layer of the multilayer network, and can reduce the consumption of resources while achieving the same transmission effect, which is of guiding significance for the planning of network lines.

The resource allocation strategy plays an important role in the improvement of network traffic capacity. In order to solve the problem of network congestion, an efficient resource allocation strategy is proposed for multilayer networks to optimize the utilization efficiency of network resources. With the proposed strategy, the network resources are allocated to nodes more reasonable and the network congestions are evidently reduced. Simulation experiments show that the proposed resource allocation strategy can greatly improve the traffic capacity of the multilayer networks compared with the average resource allocation strategy. The proposed strategy can give full play to the traffic resources of multilayer networks, which has guiding significance for optimizing the existing networks and building new networks.

In order to study traffic dynamics on multilayer networks, it is of great significance to build a network model which can more exactly reflect the actual network layered structure characteristics. In this paper, a three-layer network model in which two logical layers are mapped on one physical layer is established, and the traffic capacities of three kinds of multilayer networks with different combinations of logical layers are compared. Simulation results show that when the physical layer is the same random network, the network whose logical layers are two random networks has the optimal traffic capacity, the network with one random network and one scale-free network in the logical layers has the better traffic capacity than the network whose logical layers are two scale-free networks.