## 5 Evaluation Results
### Effects of Packet TTL on Routing Protocol Performance  
Figure 4 shows the network performance for various TTL values. First, the results for the \(PDR\) are presented in Figure 3(a). Overall, the figure shows that increasing the lifetime of packets increases the \(PDR\) to a certain point, and then it stabilizes under the HLPRP, CORP, BUBBLE Rap, and spray-and-wait routing protocols but decreases under epidemic routing and PRoPHET. CORP tries to forward the packet to the community of the destination. In a sparse network, nodes belonging to two distinct communities rarely communicate with one another. Hence, there are very few nodes that can be selected as relay nodes. As a result, CORP obtained the lowest values for the \(PDR\). In BUBBLE Rap, by using global rank (i.e., betweenness centrality), a message has a better chance of being forwarded to the destination's community. Therefore, the \(PDR\) from BUBBLE Rap is higher than CORP. The number of packet copies was not limited in PRoPHET and epidemic routing. Thus, the buffer quickly filled when the TTL increased, and a large number of packets were dropped, resulting in a low value for the \(PDR\). For example, the \(PDR\) of PRoPHET reduces from 0.6874 to 0.5363 when the \(TTL\) increases from 3 h to 6 h. In the spray-and-wait routing protocol, buffer overflow was reduced by the limited number of replications. Therefore, the \(PDR\) of the spray-and-wait is greater than that of PRoPHET and epidemic routing. By limiting the number of copies of packets, the HLPRP can also reduce buffer overflow. Moreover, relay selection is based on packet delivery predictability and social relationships. Optimal relay nodes can be found, and hence, the \(PDR\) under the HLPRP is improved and is higher than those of the other protocols. For example, when the TTL is 6 h, the \(PDR\) of the HLPRP, spray-and-wait routing, PRoPHET, BUBBLE Rap, CORP, and epidemic routing are 0.7645, 0.7450, 0.5363, 0.5335, 0.4371, and 0.4074, respectively. Figure 3: The network performance for various values of \(\alpha\). (**a**) \(PDR\). (**b**) \(PDL\). (**c**) \(DC\). Latency from various values for the packet TTL is illustrated in Figure 4b. In general, a larger value for TTL means packets can be stored in the buffer for longer, which leads to an increased \(PDL\), as shown in the figure. Under CORP and PRoPHET, a packet is slowly spread due to the absence of a rapid packet-spreading mechanism. This results in a significant increase in the \(PDL\). Based on the flooding strategy, the \(PDL\) under epidemic routing is low. In the HLPRP, packets are quickly spread during phase 1, and nodes with a higher probability of meeting the destination in a short period of time are preferred as relay nodes during phase 2. Therefore, the HLPRP also achieves a short delay, comparable to that of epidemic routing, and shorter than the other protocols. For example, when the TTL is 5 h, the \(PDL\) of the HLPRP and epidemic routing are 3476 s and 3470 s, whereas spray-and-wait routing, PRoPHET, BUBBLE Rap, and CORP are 3626 s, 3862 s, 3516 s, and 3667 s, respectively. Figure 4c shows the results for the \(DC\). Under PRoPHET and epidemic routing, the number of packet copies is not limited. As a result, the \(DC\) is extremely high. When the TTL increases, the buffer overflows, and a large number of packets are dropped. That leads to a quickly increasing \(DC\) under those protocols. In CORP, by finding the node in the destination's community before finding the destination, the \(DC\) is reduced. BUBBLE Rap uses betweenness centrality to select relay nodes until meeting nodes in the destination's community. Therefore, the number of transmissions of messages is higher than in CORP. As a result, the \(DC\) under BUBBLE Rap is higher than that under CORP. By limiting the number of replications with the spray-and-wait routing protocol, a low value of the \(DC\) can be obtained. Under the HLPRP, the number of copies of a packet in the network is also limited.