# A Congestion Control Strategy for Power Scale-Free Communication Network
## 4 Simulation Results
### Simulation Results for Integrated Routing  
If the node resources are allocated according to the node betweenness, \(\lambda=0.2\), comparing with the cognitive scale-free routing protocol [7], and the order parameter \(\eta\) vs. R under the four routing strategies are shown in Figure 13.  
In Figure 13, the critical packet generation rate of integrated routing is the largest, \(\mathrm{Rc}=62\), which shows that a larger network capacity can be obtained in the integrated routing. The results show that integrated routing can effectively enhance the traffic capacity comparing with the other routing strategies. The evolution of the total packet number Np for different R under the integrated routing is shown in Figure 14.  
Figure 12: Variations of the total load at hub nodes. Figure 13: The order parameter \(\eta\) vs. R under the four routing strategies. As shown in Figure 14, when the packet generation rate R = 62, the number of added packets can be offset by the number of packets arriving at the destination. Therefore, the number of packets in the network will be stable near a certain value. When the packet generation rate R = 63, the number of packets arriving at the destination is smaller than the added packets, so the packets are accumulated in the network, resulting in congestion or even network paralysis. It can be concluded that the critical packet generation rate of the network is 62 in the integrated routing, and the network capacity is larger, which can reduce the network congestion. The changes of maximum packet transmission time <Tmax> and the average transmission time <Tavg> vs. the packet generation rate R are shown in Figure 15.  
It can be seen from Figure 15 that when R < Rc, the maximum transmission time and the average transmission time are stable. When R > Rc, the maximum transmission time and average transmission time increase greatly, and the maximum transmission time and average transmission time in the integrated routing are less than the first two routing strategies. The path one packet traverses through with the shortest length is not necessarily the quickest way, when considering the possible traffic congestion and waiting time along the shortest paths. Hub nodes are easily selected to pass through for a packet to arrive at its destination, which causes the queues of hub nodes and the waiting time to be longer than other common nodes. Packets are delayed, and thus, the whole network gets congested. Under the global dynamic routing, the path is selected based on the current traffic load at each node, and the packets can take the bypass to avoid the congested nodes in the delivery process and reduce the degree of congestion of hub nodes. This will increase the transmission distance, but shorten the waiting time of the packets at the same time. In the shortest path routing, the transmission distance is the shortest, but the packets will easily pass through the congested hub nodes so as to continuously deteriorate the situation of node congestion, which increases the waiting time of packets and even causes data loss when the node's cache queue is full. As a result, the power system's safety and stability are severely threatened. Figure 14: Evolution of packet number Np vs. t for different R under the integrated routing. Compared with the public communication network, the power communication network is smaller. Taking the Beijing-Tianjin-Tangshan power network as an example, the number of nodes in Beijing power communication network is the largest, 533, and the number of nodes in Zhangjiakou power communication network is the smallest, 82. With the development of the smart grid, the size of the power communication network will continue to expand, and Figure 16 shows the critical packet generation rate Rc vs. the network sizes N under three routing strategies with \(\lambda\) = 0.2. In Figure 16, the critical packet generation rate of the shortest path does not change significantly as the number of nodes increases.