基于输运模型的网络相变过程

 网络相变过程需重点关注网络上的总负荷数、网络上的消失负荷数、节点的排队负荷数等指标随单位时间进入网络的负荷数R 的变化规律。为此建立了无标度网络上的输运模型，用于定量计算这3 种负荷数的变化规律。仿真结果表明：最大介数节点最先产生拥堵，导致网络的进入和消失负荷数出现不平衡，进而导致网络进入拥堵状态；当R小于临界值R_c时，网络上的消失负荷数随R同步增长。当R超过临界值R_c时，消失负荷数与R的比值持续下降，表明随着R的增加，负荷到达目的地越来越困难。

Phase Transition of Network Based on Traffic Routing Model

With the development of complex networks, more and more attentions are paid to the phase transition. The phase transition is a process of transition from a stable state to a congested state. In this process, three kinds of variations of loads on the network are involved, which are the total loads on the network, the loads removed from the network and the loads waiting for passing through some node. Firstly, based on the traffic routing model, an order parameter is introduced to characterize the phase transition. With the increase of R (the number of loads which enter into the network per unit time), this parameter experiences a transition from zero to non-zero. That is to say, there will be a critical value of R_c that characterizes the traffic phase transition from a stable state to a congested state. Secondly through the simulation, the variations of different kinds of loads on a scale-free network are identified. The node with the maximum betweenness is easily to be congested, which results in an unbalance between the loads that enter into the network and the loads that are removed from the network, and eventually results in the network congestion; When Rc, the number of loads that are removed from the network increases synchronously with R. When R>R_c, the ratio of the number of the loads removed from the network and R decreases gradually, which means that it is more and more difficult for the loads to reach their destination. Understanding the variations of the key indicators in the phase-transition process is beneficial for the effective prevention and intervention against the network.