Phase Transition of Network Based on Traffic Routing Model
SUN Lei1, LI Rong2, CHEN Xiaoguo3
1. School of Mechanics and Civil Engineering, China University of Mining & Technology(Beijing), Beijing 100083, China;
2. School of Accounting and Finance, Zhejiang Business College, Hangzhou 310053, China;
3. School of Science, Heilongjiang University of Science and Technology, Harbin 150022, China
Abstract：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 Rc 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 R<Rc, the number of loads that are removed from the network increases synchronously with R. When R>Rc, 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.
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2014, Vol. 32 
