## 3 Proposed Protocol  
In the proposed protocol, if any node receives a message from another node, the value of the delivery predictability of the receiving node to the destination node for the message is managed as preP in this paper. Then, when two nodes contact, a node with a message to send checks if the delivery predictability of the other node is higher than both the delivery predictability and the previous delivery predictability of the sending node, the message is forwarded. Otherwise, the message is not forwarded. By doing this, we introduce more restrictions on forwarding in our proposed protocol than the basic PRoPHET protocol and, thus, avoid the excessive forwarding of messages efficiently. In the proposed protocol, if a message has not been forwarded yet from a node which generated the message originally, message forwarding is carried out if the delivery predictability of the receiving node is higher than that of the sending node. This is because we need to promote message dissemination when the message is just generated and since the preP of the sending node is not defined in this case, we need to forward a message based on the basic GRTR strategy of the PRoPHET protocol. Figure 4 shows examples of forwarding in the proposed protocol compared with that of the PRoPHET protocol with the GRTR strategy. In Figure 4a, which shows the operation of the PRoPHET protocol with GRTR strategy, node S forwards messages M1, M2, and M3 to contact node B, and node  
Figure 3: The classification of related works on the extended PRoPHET protocols. B forwards message M5 to node S at T = t\({}_{0}\) based on the comparison of the delivery predictabilities of node S and node B. We assume a situation that the buffer of node B becomes full when it receives messages M1, M2, and M3. At T = t\({}_{1}\), when node B contacts node C, node C forwards message M6 and one message is dropped due to a buffer overflow. Node B forwards messages M1 and M3 to node C. At T = t\({}_{2}\), node C contacts node E and forwards messages M1, M6, and M7 to node E and receives messages M8 and M9. At this time, the buffer of node C overflows and one message is dropped. Additionally, the buffer of node B becomes full. In Figure 4b, node S forwards messages M2 and M3 and does not forward message M1, contrary to the case in Figure 4a since the preP of message M1 of node S is higher than the delivery predictability of node B at T = t\({}_{0}\). Node B does not forward message M5 to node S. At T = t\({}_{1}\), node B forwards message M3 to node C and receives message M7 from node C by comparing the delivery predictability and the preP values. Node C forwards messages M6 and M7 to node E and receives message M9 from node E at T = t\({}_{2}\). We note that message dissemination is efficiently restricted in the proposed protocol and no message drop occurs in the considered forwarding scenario, contrary to the PRoPHT protocol with the GRTR strategy, and this results in an overall performance enhancement. Figure 4: Examples of the forwarding scenario. (**a**) PRoPHT with GRTR, (**b**) Proposed protocol. Figure 5 shows the flowchart of the proposed protocol. When two nodes A and B contact, they firstly exchange summary vectors which include information of the messages they have in their buffer and all the delivery predictability values of each node to all other previously contacted nodes. We note that the values of preP are not exchanged during contact. Then node A chooses a message which does not exist in node B. If the destination of the message in node A is node B, it is delivered to node B. Otherwise, node A compares the delivery predictability of itself with that of node B. If P(A,D) is larger than P(B,D), the message is not forwarded to node B. If P(A,D) is not larger than P(B,D), node A checks if preP(A,D) exists. We note that if the message is generated in node A originally and has not been forwarded to another node before, that is, preP(A,D) does not exist.