4.3.1. Methodology

In a real environment, each node is selfish. To make the simulation experiment closer to the real scene, we randomly set the selfishness of the node relative to other nodes in the experiment. When a node forwards a message, it forwards the message according to a certain cooperation probability that removes the selfishness. It should be emphasized that we aim to select nodes that have a high probability of encountering the target node and are willing to cooperate to forward the message. In the experiment, the cooperation matrix of the algorithm was not set manually, but was based on the cooperative probability calculated by the number of times the node helps a node to forward the message in the previous *T* period.

The evaluation of the model mainly comes from two aspects: (1) Effectiveness analysis. The experiment compares the difference between our presented model and other existing models in optimizing the network structure and improving the information delivery ratio. (2) Adaptability analysis: The probability matrix is periodically updated by various dynamic change information, and the nodes that can cooperate and have a high probability of encountering with the destination node are filtered to transmit data, thereby increasing the delivery ratio and reducing the average hop count. As a reference, we set a list of performance metrics, which is used for comparison, as follows:


3. Hop count is the average hops of successfully delivered messages.

We use these performance metrics to analyze the effects of the model and compare them with other researchers' proposed solutions. To compare the performance of the PEBN protocol with other schemes, the delivery ratio, overhead ratio, and hop count were measured.

### 4.3.2. Impacts on Delivery Ratio

Figures 5 and 6 shows the delivery performance of the PEBN protocol when the number of nodes and simulation time are different, respectively. From Figure 5 we can see that the delivery ratio of messages by the PEBN protocol is higher than other schemes due to better choices while sending the messages. This is because our solution sets a different degree of selfishness to each node for other nodes. Other schemes can easily lead to message loss, because they cannot fully consider the cooperating factors and social relationship factors of the nodes, and even cannot ge<sup>t</sup> more information about the nodes. Therefore, our algorithm can obtain more accurate predictions to have a better choice in the process of screening nodes. Moreover, as the number of nodes increases, the training of the prediction matrix is more extensive and accurate due to the increase of node social information. Thus, obtaining more unknown information between nodes, increasing the number of candidate nodes in the information transmission process, and improving the accuracy of node selection, thus makes it more likely to select the optimal node. From Figure 6, it can be observed that the delivery performance of the PEBN protocol is better than the other scheme. Because we not only consider the probability of encountering the target node, but also the path of the target node, it is unlikely to lose the packet. In addition, as the simulation time increases, the message delivery rate also increases, and the message will have more time to wait for the next best node.

**Figure 5.** The relationship between the number of nodes and the delivery ratio.

**Figure 6.** The relationship between time and delivery ratio.

### 4.3.3. Impacts on Average Hop Count

Figures 7 and 8 shows the hop count of the PEBN protocol when the number of node and simulation time varies, respectively. In Figure 7, the average hop count of the protocols is compared with others schemes. The PEBN protocol has the smallest average hop count in the compared scheme because it optimizes the routing of message transmissions more efficiently than other schemes. It can be seen in Figure 7 that as the number of nodes increases, the average hop count of the node increases and then gradually stabilizes. Our solution considers many factors, and as the number of nodes increases, the relationship between nodes becomes more complex, and more hidden features between nodes are mined through probabilistic prediction models, thus reducing the number of hops from the source node to the destination node. However, other methods may not have many parameters to enhance the adaptability of the model. Therefore, our model performs better. From Figure 8, it can be observed that our proposed scheme has fewer hops than other schemes. This is because our solution collects and processes node feature information, so we can ge<sup>t</sup> as much data as possible to more accurately predict the probability of encounters between nodes. As the simulation time increases, the node can capture more information about the movement of the nodes, which can add more additional information to the process of selecting the key nodes, making the model more robust. Therefore, the average hop count of the node is gradually reduced and stabilized.

**Figure 7.** The relationship between the number of nodes and hop count.

**Figure 8.** The relationship between time and hop count.

### 4.3.4. Impacts on Routing Overhead

Figures 9 and 10 shows the routing overhead of the PEBN protocol when the number of nodes and simulation time are varied, respectively. From Figure 9, it can be observed that the routing overhead of our scheme is compared with other schemes. Compared with the result, PEBN has a better performance than other models. Since we apply the node cooperation to our proposed model, we can also perform well in scenarios where the node has selfish features. PNEC can predict transmitting neighbors better than other models; the message will be forwarded to a node with a high probability of satisfying the destination in the transmission route, which effectively reduces the cost loss of sending the message to the non-cooperative node. In addition, we can also observe that as the number of nodes increases, the amount of routing overhead also increases. An increase in the number of nodes means the number of candidate nodes for message selection increases. Messages need to be passed to more nodes, thereby increasing the overhead of information being propagated over the network. Moreover, this same observation can be seen in Figure 10, which shows that routing overhead increases as the simulation time is increased. Because the nodes do not need to continuously calculate and decide through the proposed model during the information transmission process, the transmission task of nodes becomes simpler. Furthermore, we have more complex probability models to choose neighbors, so our overhead increase ratio is relatively smaller than other models with the increase of simulation time.

**Figure 9.** The relationship between the number of nodes and overhead.

**Figure 10.** The relationship between time and overhead.

The conclusion can be drawn by comparing the three indicators of several schemes with the number of nodes and the simulation time. The PEBN algorithm adds social relationships and cooperation relationships when predicting probabilities so that a node can deliver a message to a cooperating node that has a high probability of encountering a destination node. Experiments show that the PEBN algorithm outperforms other algorithms in terms of the transmission success rate, routing overhead, and hop count. Specifically, the algorithm not only improves the data transmission efficiency in the network, but also adopts the updated information to adapt to the current network environment when the network topology changes dynamically. In addition, handling complex transmission decisions through base stations or edge devices reduces the node overhead. By combining the social and cooperative relationships between nodes with a probabilistic prediction model, a better transmission path can be selected to reduce the number of hops to the destination node. Therefore, our scheme can improve performance in the transmission environment.
