Analysis of network traffic flow dynamics based on gravitational field theory

For further research on the gravity mechanism of routing protocol on complex networks, we introduce the concept of routing awareness depth, represented with ρ . On this basis, we define the calculating formula of the gravity of the transmission route for the packet, and propose a routing strategy based on gravitational field of node and routing awareness depth. In order to characterize the efficiency of the method, we introduce an order parameter η to measure the throughput of the network by the critical value of phase transition from free flow to congestion, and use the node betweenness centrality B to test the transmission efficiency of the network and congestion distribution. We simulate the network transmission performance under different values of routing awareness depth ρ . Simulation results show that if the value of routing awareness depth ρ is too small, the gravity of the route is composed of the attraction of very few nodes on the route, which cannot improve the capacity of the network effectively; if the value of routing awareness depth ρ is greater than the network's average distance <l>, the capacity of the network may be improved greatly and no longer change with the sustainable increment of routing awareness depth ρ , the performance of the routing strategy enters into a constant state; moreover, whatever the value of routing awareness depth ρ is, our algorithm always effectively balances the distribution of betweenness centrality and realizes the equal distribution of network load.