As demonstrated in Table 3
, the average delivery ratio from MSNN increases by 15%, 60%, 7% and 6% as compared with those from spray and wait, Epidemic, ICMT and EIMST, respectively. Alternatively, the average end-to-end delay from MSNN decreases by 90%, 75%, 67% and 50% as compared with those from spray and wait, Epidemic, ICMT and EIMST, respectively. Finally, the average network overhead from MSNN reduces by 68%, 44%, 24% and 13% compared with those from spray and wait, Epidemic, ICMT and EIMST, respectively. Overall, the MSNN algorithm is superior to other four approaches in terms of delivery ratio, average end-to-end delay and average network overhead.
This is because that the MSNN algorithm mainly divided into four continuous phases. First, to achieve the functional integrity of the algorithm, it is necessary for mobile nodes to acquire network routing state. Secondly, the mobile similarity of the nodes is calculated by the relationship among nodes. Thirdly, the retained nodes are selected by the clustering algorithm, and the distance between the Minkowski distance and the MVD distance is calculated, and the distance of the social attribute is calculated according to the social attribute. Finally, the relay node with the highest probability of message forwarding success is selected as suitable relay nodes in data dissemination process.
4.2.1. Performance of MSSN Algorithm under Different Mobile Similarity Thresholds
This section mainly describes the performance of the MSSN data transmission strategy under different mobile similarity thresholds. The purpose of setting the mobile similarity threshold is to reduce the number of neighbor nodes that perform the next step of calculating social similarity with the destination node, thereby reducing the calculation workload of the next step to reduce the delay and improving the reliability and accuracy of the obtained relay node. Therefore, the value of mobile similarity determines the range of relay nodes selected according to the node social similarity in the second step, which has a significant influence on the transmission performance of the MSSN algorithm. According to the simulation experiment results, when the mobile similarity threshold between the neighbor node and the destination node is set to 0.54–0.55 the MSSN data forwarding strategy shows the optimal performance in the transmission environment.
First, we explore the impact of the mobile similarity threshold on the delivery ratio. As show in Figure 5
, when the mobile similarity threshold is from 0.15 to 0.55, the delivery ratio is in a rising state, and the highest value even reaches 0.91, but the rising range gradually decreases. When the mobile similarity threshold rises from 0.55 to 0.75, the delivery ratio drops sharply, and even drops to 0.79. When the mobile similarity threshold rises, we no longer consider those nodes with lower similarity to the destination node. At the same time, after removing those nodes with lower mobile similarity, the higher the accuracy and reliability of the relay nodes obtained by the next step of calculating the social similarity operation. However, when the mobile similarity is higher than a certain value, some neighbor nodes that may also be suitable relay nodes are removed although more reliable relay nodes can be obtained, Consequently, the number of relay nodes we obtain is small, which leads to a lower delivery ratio.
shows the effect of the mobile similarity threshold on the average end-to-end delay. As shown, when the mobile similarity threshold rises from 0.15 to 0.55, the average end-to-end delay drops from 98 to 80, and its downward trend tends to be flat. That is because as the mobile similarity threshold increases, neighbor nodes that are almost impossible to become reliable relay nodes due to the small similarity of movement to the destination node are removed, thereby greatly reducing the delay of routing selection. Since some noise nodes are reduced, the message carrier can find the appropriate relay node faster and forward the message out, the average end-to-end delay is reduced. However, when the mobile similarity threshold is higher than 0.55, the average end-to-end delay increases rapidly, even reaching 95, and the upward trend is increasing. That’s because when the mobile similarity threshold exceeds a certain level, the probability and number of suitable relay nodes will be reduced due to the large number of neighbor nodes being abandoned, and the probability of destination node receiving messages will be reduced, leading to high average end-to-end delay.
Finally, the effect of different mobile similarity thresholds on the overhead on average is shown in Figure 7
. As we can see, when the mobile similarity threshold increases gradually from 0.15 to 0.55, the average cost decreases rapidly and even drops to 183. However, when the mobile similarity threshold continues to increase from 0.55, the average cost shows a certain upward trend, but the rate of increase is relatively slow. That’s because when the mobile similarity threshold is around 0.55, we no longer consider the neighbor nodes that are not suitable as reliable relay nodes because of the low mobile similarity between them and the destination node, thus reducing the memory and processing resource overhead needed in computing. At the same time, we can get more reliable relay nodes, which increases the success rate and speed of destination node to get the message, and thus reduces the average network overhead. And when the mobile similarity threshold continues to increase on the basis of 0.55, as the threshold of most nodes is lower than this value, the range of neighbor nodes from which we choose reliable relay nodes decreases sharply, so that the number of reliable relay nodes we can obtain decreases and the overhead on average increases.
4.2.2. Comparison Result Analysis between Algorithms under Different Number of Nodes
This section mainly compares and analyzes the performance of the five algorithms mentioned above under different number of nodes. For those routing algorithms based on contextual message in opportunistic social networks, the message carrier needs to forward the message to multiple relay nodes. When the number of neighbor nodes around the message carrier is insufficient, it may not be able to select a plurality of suitable relay nodes from the neighbor nodes to perform effective data transmission. Therefore, in this experiment, we reasonably set the number of neighbor nodes as a variable to study the transmission performance of each algorithm. In addition, the comparison results show that the MSSN algorithm performs better than other algorithms in terms of delivery ratio, average end-to-end delay and overhead on average under different node numbers.
As demonstrated in Table 4
, the average confidence levels of delivery ratio, end-to-end delay and network overhead from the MSNN algorithm are 0.85, 0.92 and 0.95, respectively. Alternatively, the average confidence interval of delivery ratio, end-to-end delay and network overhead from the MSNN algorithm are 0.4–0.95, 0–65 and 25–200, respectively. This indicates that the probability that the real value obtained in this simulation falls in the estimated value interval is relatively large, and the experimental data obtained from this experiment are also relatively reliable. Compared with spray and wait, Epidemic, ICMT and EIMST, the improved results reflected by the experimental data are more reliable. Next, we compare the proposed approach with spray and wait, Epidemic, ICMT and EIMST in terms of delivery ratio, end-to-end delay and network overhead, respectively.
Above all, we evaluated the delivery ratio of each algorithm under different number of nodes, and the comparison results of the five algorithms are shown in Figure 8
. As shown in the figure, with the increase of the number of neighbor nodes from 100 to 700, the delivery ratio of most routing-forwarding algorithms shows a certain upward trend. However, the delivery ratio of Epidemic algorithm shows a downward trend when the number of nodes exceeds 300. This is because the Epidemic routing algorithm adopts information flooding mechanism to carry out information transmission, and when the number of nodes exceeds a certain range, it may cause network congestion, resulting in a lower delivery ratio.
With the increase of the number of neighbor nodes from 100 to 700, we can see that the average delivery ratio of the MSSN algorithm increases by 15%, 60%, 7% and 6% as compared with those from spray and wait, Epidemic, ICMT and EIMST, respectively. Especially, when the number of mobile nodes in communication area fluctuates from 200 to 300, the delivery ratio of MSSN algorithm is very close to those from EIMST approach. This is because both of the two algorithms are based on information exchange between a pair of nodes and community division, in which frequent information exchange between nodes in the same community is beneficial to promote the delivery ratio in the networks, and the effective strategy of message duplicates controlling is able to reduce the average end-to-end delay and network overhead in the networks. Moreover, when the number of nodes reaches 700, the delivery ratio even reaches 0.93. The MSSN algorithm comprehensively utilizes the mobile and social similarities between the neighbor nodes and the destination node. When the number of neighbor nodes increases, the message carrier can find more reliable relay nodes to perform efficient data transmission, thereby increasing the delivery ratio.
The “Spray and Wait” algorithm performs a certain number of copies of the message in the network. When the number of neighbor nodes increases, the probability of encounter between neighbor nodes and destination node will increase, so the delivery ratio gradually rises from 0.45 to 0.84. The ICMT and EIMST algorithms achieve effective data transmission through cooperation between multiple nodes, but this is not an effective data transmission scheme when the cache space of nodes is limited. Therefore, compared with traditional algorithms, these two algorithms have some improvement in delivery ratio. When the number of nodes is 700, the transmission rate of ICMT algorithm even reaches 0.9. However, in general, the delivery ratio of MSSN algorithm is the highest among these algorithms.
In Figure 9
, we show the performance of the average end-to-end delay for each algorithm under different number of neighbor nodes. As we can see, in addition to the Epidemic algorithm and the Spray and Wait algorithm, the average end-to-end delay of other algorithms shows a gentle downward trend as the number of nodes increases. The reason why the average end-to-end delay of Spray and Wait has been rising is because the algorithm uses the mechanism that randomly transmits the replication of the message to the network to implement data transmission. When the number of nodes increases, the probability of the randomly distributed message reaching the destination node is reduced, so the average end-to-end delay rises from 68 to 123. As for the Epidemic algorithm, since the algorithm adopts the flooding data transmission mechanism, when the number of neighbor nodes exceeds 400, the replication of messages in the network increases sharply, thereby causing network congestion, and thus, the average end-to-end delay increases.
We can see that the average end-to-end delay of MSSN algorithm always stays at the lowest state from 63 to 20 when the number of nodes increases from 100 to 700. That is because when the number of neighbor nodes increases, the number of reliable relay nodes that the MSSN algorithm can find based on the mobile similarity and social similarity between nodes increases, and the average end-to-end delay decreases. The ICMT algorithm utilizes the cooperation mechanism between nodes to realize the effective transmission of data, and the EIMST algorithm carries out message forwarding through effective information management and community division. Therefore, compared with other two traditional algorithms, these two algorithms have higher average end-to-end delay. To sum up, compared with other algorithms, the MSSN algorithm is the best method to reduce the average end-to-end delay of network message transmission.
The performance of each algorithm in terms of overhead on average with different number of nodes is shown in Figure 10
. As the number of neighbor nodes increases from 100 to 700, the overhead on average of all the other four algorithms except the Epidemic algorithm is in a slowly decreasing state. Moreover, the overhead on average of the MSSN algorithm has been kept below 200. When the number of nodes is 700, the average overhead from the MSSN algorithm is even reduced by 68% as compared with those from spray and wait, and it is very close to those from the EIMST algorithm. The reason why the MSSN algorithm can always maintain a low overhead on average is mainly because the algorithm comprehensively utilizes the mobile node similarity and social attributes of the neighbor nodes to select reliable relay nodes, which is similar with the EIMST algorithm. When the number of neighbor nodes becomes larger, the relay nodes determined by the MSNN algorithm are more accurate and more numerous so that messages can be forwarded faster. The reason why the overhead on average of the Epidemic algorithm has been increasing is mainly because the algorithm uses the message flooding mechanism. When the number of nodes increases, the replication of messages in the network increases sharply, and the destination node cannot quickly obtain messages, which results in a larger average network overhead.
The ICMT algorithm utilizes the cooperation mechanism between neighbor nodes and establishes a method of identifying nodes by relying on the probability of encounter. Therefore, when the number of nodes increases from 100 to 700, the average cost of the algorithm shows a certain downward trend. the average network overhead from MSNN reduces by only 13% compared with those from EIMST. To be specific, the EIMST algorithm uses community division and information management to perform an efficient data transmission process. In the same way, the mobile similarity and social similarity between nodes are also used in the MSSN algorithm, which is mainly based on the moving trajectories of nodes, the number of common neighbor nodes and their social attributes. Besides, communities share some parts of transmission missions, nodes carrying messages may reduce overhead. Therefore, when the number of nodes increases, the average cost of the algorithm gradually decreases from 224 to 86. In conclusion, The MSSN algorithm outperforms other algorithms in terms of network overhead when the number of nodes changes.