## 3 The Proposed Routing Mechanism
### Mobility Model  
In this paper, the system under the study is a social DTN, where each mobile node is in continuous movement. To simplify the problem, we have adopted the mobility model described in [8] with some modifications, because the model can reflect the characteristics of the scenarios (campus, international conference) which have been investigated in this paper. The model in [8] can accurately reflect the characteristics of the scenarios but it has not made full use of the characteristics of the nodes. According to the analysis in [15], there are approximately 20% of the nodes which have extremely high relaying ability. That is to say, these 20% nodes are more active than other nodes. Therefore, to accurately describe the characteristics of the nodes, 20% of the nodes have been set to be active than other nodes in the modified mobility model. In the system, there are five hot spots and one cold spot denoted as \(H_{1}-H_{5}\) and \(C\) as shown in Figure 1. Each mobile node is assumed to have a \"home\" hot spot where it stays most of its time but not all the hot spots. And each mobile node always goes to the cold spot when it leaves a hot spot. For any node \(a\) (assume it belongs to the hot spot \(H_{I}\)), we assume when it leaves \(H_{I}\), it always goes to the cold spot. The assumption is to make the model closer to the reality. For example, in a campus scenario (one of scenarios in social DTNs), a hot spot may be a department where students stay together, while a cold spot would correspond to the transition between two hot spots. In other words, before entering other hot spots, node \(a\) needs have a transition process when it leaves \(H_{I}\). It is further assumed that 20% of the nodes will take more time to move among different spots than other nodes. As shown in Figure 2, when a node is home, it will have a probability of \(P_{H}\) to stay or \(1-P_{H}\) to move to the cold spot in the next time slot. While at the cold spot, it will go home with probability of \(P_{H}\), or have a probability of \(P_{C}\) to stay, or move to other hot spot with probability of \(1-P_{H}-P_{C}\), where \((P_{H}+P_{C}<1)\). Finally, when the node stays at a hot spot which is not its home, it will have a probability of \(P_{H}\) to move to the cold spot or stay with probability of \(I-P_{H}\). The WiFi technology has been adopted for the communication among these nodes. Each node will have a unique ID and maintain the contact information with others by a list of parameters including node ID, contact probability, and contact time. The parameter of the contact probability is automatically updated in each time slot according to the contact time. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Quantity** \\ \hline \(\varepsilon_{ij}\) & Contact Probability between node \(i\) and \(j\) \\ \(a\) & A const value between 0 and 1 \\ \(\gamma\) & Clustering threshold \\ \(C_{i}\) & The cluster which includes node \(i\) \\ \(S_{i}\) & The stability of node \(i\) in \(C_{i}\) \\ \(M_{i}\) & Members in \(C_{i}\) which are recorded by node \(i\) \\ \(T_{i}^{\prime}\) & Contact time between node \(i\) and \(j\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of Notations. Based on the mobility model, some communities can be formed from time to time in the system and nodes within the same community contact frequently with each other. The message forwarding inside one community is simple. On the other hand, mobile nodes in different communities have little contact but there exist some active nodes moving among communities which can be used to transmit messages from one community to another as relay nodes. As a result, clustering technology can be adopted in our new routing protocol, CCS-DTN. And different forwarding mechanisms could be used for the intra-cluster and the inter-cluster routing. By the clustering technique, each node will belong to a cluster with a cluster ID and maintain the information of the members in the cluster by a list of parameters such as the node ID.