基于引力场理论的复杂网络路由选择策略研究

Routing strategy for complex networks based on gravitation field theory

利用引力场理论对网络传输过程中节点激发的引力场进行了描述,建立了节点的引力场方程,引入α和γ两个参数,用于调节数据传输对节点畅通程度、节点传输能力和路径长度的依赖程度.基于节点的引力场,提出了一种高效的路由选择算法,该算法下数据包将沿着所受路径引力最大的方向进行传递.为检验算法的有效性,引入有序状态参数η,利用其由自由流到拥塞态的指标流量相变值度量网络的吞吐量,并通过节点的介中心值B分析网络的传输性能和拥塞分布.针对算法在不同α,γ取值条件下的路由情况进行了仿真.仿真结果显示,与传统最短路由算法相比,本文算法将网络传输能力提高了数倍,有效地均衡了节点的介中心值分布,传输路径平均长度Lavg随负载量R的增加表现出先增后减的变化趋势,而参数α与γ值的变化对网络传输能力几乎没有影响,说明本文路由算法的性能不依赖于α与γ,对于可行域内任意的α与γ,算法都能保证网络传输能力近似相等.

Using the theory of gravitational field, we study the gravitational field induced by the node in the process of the network trans- mission, establish the gravitational filed equation, and define two parameters α and γ for adjusting the dependencs of transmission data on the unblocked degree of node, the transmission capacity of node and the path length. Based on the gravitational field of node, an efficient routing strategy is proposed, and the package will be transferred along the route with maximum gravitation. In order to characterize the efficiency of the method, we introduce an order parameter ηto measure the throughput of the network by the critical value of phase transition from free state to jammed state, and use the node betweenness centrality B to test the transmission efficiency of network and the congestion distribution. We simulate the network transmission efficiencies under different values ofα and γ Sim- ulation results show that compared with the traditional shortest routing strategy, our routing strategy improves the network capacity several times, and effectively balances the distribution of the betweenness centrality of nodes, and the average path length （Lavg） shows a trend from ascent to descent with the increase of load amount R, and the change of the parametersα and γ nearly have no effect on the network transmission capacity, which suggests the efficiency of our routing strategy is independent of α and γ the network capacities are approximately equal for any values of α and γ in the feasible region.