## 5 Adaptive Scheduling Mechanism Based on Self-Similarity
### The Proposed ASMSS  
The work in [28] has shown that each node can predict future contact information based on its history contact information. For a given node, we define its expected Encounter Value (\(EV\)) as the number of nodes that it may encounter in the future. In this paper, we design the _ASMSS_ based on expected encounter value. In order to calculate the expected \(EV\), we divide the period \(T\) into \(s\) slots, and the length of each slot is \(T_{slot}=T/s\). Then each node can calculate the \(EV\) in each slot at the beginning time of the period and denote to be \(EV_{i}(x),\forall i\in N,x\in[1,s]\). For the \(EV\) calculation, each node should keep records of the contact times with other nodes and then calculate and store the inter-contact intervals in the node buffer. We take an example of node \(i\), the intercepted \(m\times n\) history inter-contact intervals with node \(j\) are denoted as \(\Gamma_{ij}=\{\chi_{ij}^{1},\chi_{ij}^{2},\cdots,\chi_{ji}^{mn}\}\). Then, we use the _LMMSE_ predictor to predict the coming inter-contact interval with the \(\Gamma_{ij}\). Assuming the predicted result between nodes \(i\) and \(j\) is \(t_{ij}\), the last contact time is \(t_{ij}^{0}\), and the beginning time of a certainperiod is \(t(t>t_{ij}^{0})\), we can calculate the value of \(x\), which means node \(i\) and node \(j\) are expected to encounter with each other in the \(x\)th slot of this period, based on the Equation (5). Also, the \(EV_{i}(x)\) can be calculated with the value of \(x\) based the Equation (6). Finally, node \(i\) can get the final result of \(EV_{i}(x)(x\in[1,s])\) in each slot with all encountered nodes taken in account. \[x=(t_{ij}-(t-t_{ij}^{0}))/T_{slot} \tag{5}\]  
\[EV_{i}(x)=\left\{ \begin{array}{c}EV_{i}(x)+1,1\leq x\leq s\\ EV_{i}(x)\quad,\quad x>s\end{array} \right. \tag{6}\]  
According to the _LMMSE_ predictor and Equations (5) and (6), each node in the network can get the expected \(EV\) in each slot of a certain period. Then, each node can choose \(T_{w}\) slots to be in listening state, and these \(T_{w}\) slots have the highest value of the expected \(EV\). This process will be repeated at the beginning time of each period, and each node can adaptively configure its scheduling mechanism at the beginning time of each period. The process flowchart of _ASMSS_ can be shown in Figure 3.  
For ease of understanding, we provide an example for the scheduling mechanism of node \(N_{0}\). It is assumed all nodes that ever encountered with \(N_{0}\) to be \(H=\{N_{1},N_{2},\cdots,N_{10}\}\) at the beginning time of  
Figure 3: The flowchart of the _ASMSS_. a certain period. There are 10 slots in each period, and \(T=300\) s, \(T_{slot}=30\), \(D=30\%\). Then, the next inter-contact interval of each node pair can be figured out based on the _LMMSE_ predictor, and the slots expected to encounter neighbours can be calculated with Equation (5). If \(N_{0}\) and \(N_{1}\) are expected to encounter with each other in the second slot of this period, it can be expressed as \(x\{N_{0},N_{1}\}=2\). Similarly, we have \(x\{N_{0},N_{2}\}=4\), \(x\{N_{0},N_{3}\}=2\), \(x\{N_{0},N_{4}\}=7\), \(x\{N_{0},N_{5}\}=9\), \(x\{N_{0},N_{6}\}=7\), \(x\{N_{0},N_{7}\}=2\), \(x\{N_{0},N_{8}\}=4\), \(x\{N_{0},N_{9}\}=null\), \(x\{N_{0},N_{10}\}=7\), where \(null\) represents that \(N_{0}\) and \(N_{9}\) will not encounter in this period. Based on Equation (6), we can get the \(EV_{N_{0}}(1)=0\), \(EV_{N_{0}}(2)=3\), \(EV_{N_{0}}(3)=0\), \(EV_{N_{0}}(4)=2\), \(EV_{N_{0}}(5)=0\), \(EV_{N_{0}}(6)=0\), \(EV_{N_{0}}(7)=3\), \(EV_{N_{0}}(8)=0\), \(EV_{N_{0}}(9)=1\), \(EV_{N_{0}}(10)=0\). Finally, we can choose three slots with the highest value of \(EV\) to be listening state according to the value of \(D\), which are slots 2, 4 and 7 respectively.