## 3 Performance Evaluation Results and Discussion
### Effects of the Node Density  
The simulation work here aims to explore the impact of changes in the number of nodes on protocol performance. The variation range of the number of nodes in this simulation is 100-600, and Table 4 shows other necessary simulation parameters. Figure 16 shows the trend of packet delivery rate of different protocols with varying numbers of nodes. The packet delivery rate of the five protocols gradually increases with the increase in the number of nodes. The reason is that the node number significantly affects network density. When the node density is low, the number of nodes contained in the forwarding area of each forwarding node is also quite small, which may cause a routing void and interrupt data transmission. Traditional protocols have not taken specific measures to address the routing void, resulting in a lower packet reception success rate. This is a common problem that may be encountered when the network density is low. The FLRAF protocol can evaluate the link quality between nodes to select nodes with good transmission conditions, but it cannot effectively address the issue of routing void. Therefore, when the number of nodes is small, a high data packet delivery rate cannot be guaranteed either. As node density rises, more nodes are available in each forwarding area, which boosts the chances of the routing protocol successfully finding the next hop node. Therefore, the problem of data transmission interruption will be greatly improved, and the packet delivery rate will gradually increase. Figure 15: Effects of \(\alpha\) on network lifetime. Figure 17 shows the trend of the network average end-to-end delay of different protocols as the number of nodes changes. Thanks to the fuzzy reasoning system added to the FLRAF protocol, the effective advance distance is taken into account when selecting nodes. Therefore, in the process of selecting nodes, nodes at the edge of the transmission range are given more priority while maximizing compliance with the SNR requirement. This may maximize the efficiency of multihop transmission by reducing the number of hops that data packets pass through from source to sink. Thus, the FLRAF method reduces the average end-to-end delay compared to most traditional protocols. However, its delay performance is inferior to the GTRP method due to the use of fuzzy reasoning in evaluating link quality. It is necessary to transmit probe packets to complete the task of evaluating link quality. This process introduces additional processing delay, partially offsetting FLRAF's advantage in reducing transmission latency. This is a problem that needs to be considered in the later stage. Figure 18 shows the trend of network average energy consumption of different protocols with varying numbers of nodes. In terms of energy consumption, as the number of nodes increases, the total energy consumption of the network will inevitably increase gradually. This is because, in the process of one-hop transmission, the higher the network density, the greater the number of nodes involved in receiving the data packets sent by the forwarding nodes of the previous hop, which will inevitably result in higher energy  
Figure 16: Effects of node density on packet delivery rate. Figure 17: Effects of node density on end-to-end delay. consumption. On the other hand, because the average energy consumption of the network is determined by dividing the total energy consumption of the network by the number of data packets successfully received by the receiving node, and due to the difference in the speed of increase between the total energy consumption of the network and the number of successfully received data packets, the average energy consumption shows a gradual upward trend. Figure 19 shows the trend of the network lifetime of different protocols with varying numbers of nodes. The network lifetime extends with the increase of the number of nodes. Traditional protocols do not have a node selection process for energy management, and the network lifetime will not change significantly.