## 2 Related Works  
Related works on general delay tolerant networks protocols have been already covered by the survey papers [10; 11; 12; 13; 14], where the authors classified and compared related protocols in detail. Since the main focus of our paper is related to the PRoPHET protocol, we review related works on the extension of PRoPHET protocol for performance enhancement. A lot of works related to PRoPHET protocol have been carried out [15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. In Reference [15], the number of message copies is limited by using the sociality of nodes in order to improve the performance of the proposed protocol. In Reference [16], the buffer is managed by controlling the delivery predictability based on the number of message copies in order to solve the network performance degradation problem due to excessive copies of a message. In Reference [17], either Epidemic or PRoPHET is selected based on the density of nodes. That is, if the number of simultaneous contacts is smaller than a threshold, the Epidemic protocol is applied. Otherwise, the PRoPHET protocol is applied. By doing this, the appropriate protocol, either Epidemic or PRoPHET, is selected dynamically based on the density of the neighboring nodes. In Reference [18], contact duration, which is the time duration that contact is maintained, and the contact frequency are also considered in the calculation of the delivery predictability for an efficient message delivery. In Reference [19], the AntPRoPHET scheme was proposed, where ant colony optimization, which is one of the nature-inspired optimization technique based on the behavior of ant, was applied to the PRoPHET protocol in order to optimize the performance of the PRoPHET protocol. In Reference [20], in order to reduce unnecessary message forwarding, the message is forwarded only when the delivery predictability of the receiving node is larger than the sum of the delivery predictability of the sending node and a minimum threshold value, and the sum of delivery predictabilities of the receiving nodes so far is less than a predefined threshold value. In PRoPHET+ Reference [21], a new metric, deliverability, which is defined as a weighted sum of battery power, location, popularity, buffer size, and the delivery predictability was proposed. In Reference [22], hop count traversed by a message as well as delivery predictability are considered to determine the next hop node. In Reference [23], the distance-based PRoPHET protocol was proposed, where the distance between any two nodes was considered additionally in order to calculate the delivery predictability. In Reference [24], a node selects a node located in the smallest distance as a forwarder in order to transmit with the highest rate. In Reference [24], the authors extended the algorithm in Reference [23] by additionally considering the community mobility model, where the random waypoint mobility model was considered in Reference [23]. In the history encounter-based spray and wait (HESnW) protocol [25], the multiple probabilities from node S to node D are defined as the multiplication of delivery predictability from node S to node H, which is a history node that node S ever contacted before, and delivery predictability from node H to node D. Then, a message is forwarded to a node in the spray phase, either if the node has a higher delivery predictability or if the node's multiple probability is higher than the delivery predictability of the sending node when the deliver predictability of the node has higher than the transfer threshold. In Reference [26], the authors proposed an improved PRoPHET protocol using the context information of the node such as the average distance and time from the reception to the delivery of a message.