## 3 System Model Design
### Collecting Enough Information about the State of the Network  
In our proposed strategy, there exists a special warming-up period in which each node gains and updates adequate and accurate information about the state of the network. The information about the state of the network is collected and updated only at the warming-up phase, meaning this phase is actually a period for data collection and updating. The length of the warming-up phase \(\Delta T\) is generally set according to the user's activity cycle [15]. In the real social scene, users are more likely to repeat the same mobile route every day, such as from places of residence to workplaces, and there is a high probability of meeting the same person each day [16]. Therefore, the optimal value for the warming-up phase in the real social scene should be set to 24 h. After the warming-up phase, message carriers begin to make suitable message delivery decisions by the fuzzy evaluation of social and mobile similarities of nodes in the network. Moreover, in order to quantify the whole process of information collection and updating in the warming-up phase, we define the following Equations (1) and (2) as the state sequence of node \(u\). \[List(u)=<GP_{u},\gamma_{u},*List_{m}> \tag{1}\]  
\[*List_{m}=<List(b),List(c)\cdot\ldots\cdot List(n)> \tag{2}\]  
where \(GP_{u}\) represents the mobile distribution of the node \(u\), and \(\gamma_{u}\) represents a feature vector of the node \(u\) that includes different social attributes of this node. \(*List_{m}\) is a state sequence set of the other nodes encountered by the node \(u\) in a given warming-up period \(\Delta T\). Meanwhile, if a node \(u\) meets another node \(v\), we adopt the following Equation (3) to construct a table item \(List(1)\) for the meeting information between nodes \(u\) and \(v\). Moreover, the encounter status matrix \(S(n)\) for all table items can be established by the following Equation (4). \[List(1)=List(u)\ll=\gg List(v)=<GP_{u},\gamma_{u},GP_{v},\gamma_{v},*List_{m}> \tag{3}\]  
\[S(n)=(List(1),List(2),List(3)\ldots List(n)) \tag{4}\]  
Consequently, during the warm-up period, each node adopts its own mobile information, social attributes, and historical meeting information to build a state sequence \(List\). As there are movements of nodes in the network, when a node encounters another node, the two nodes update their own \(*List_{m}\) through the state sequence information obtained from each other. Furthermore, the information exchanging process can also be completed through the cooperation of multiple nodes in the network. For each encounter between nodes, this scheme builds a table item that contains all information about the meeting of the two nodes. Moreover, in order to establish a unified data set about the node similarity, the encounter status matrix \(S(n)\) will be built in a given warming-up period \(\Delta T\). Unlike the social attribute of nodes in the network, the mobile information changes over time, so promptly updating the mobile information of users can facilitate the timeliness, uniformity, and accuracy of the statistics collected. More specifically, as shown in Figure 1, when node \(u\) encounters node \(v\), the node \(u\) sends \(List(u)\) to the node \(v\), and the node \(v\) also transmits its own state sequence \(List(v)\) to the node \(u\). Moreover, through the state sequence obtained from each other, the two nodes update their own encounter status matrix \(S(n)\) by adding this meeting information \(List(1)\) to their own cache spaces. As there is movement of nodes in the network, the node \(u\) may encounter another node \(w\), and the two nodes will continue to update the encounter status matrix \(S(n)\), which effectively establishes a unified dataset about the state of the network. After the warming-up period \(\Delta T\), message carriers start to make suitable message delivery decisions by the fuzzy evaluating of social and mobile similarities of nodes in the network.