## 4 Scheduling
### Analysis of Energy Consumption  
In this section, we compare the energy consumption between mode 4 of B-MAC and our modified scheduling scheme. Ignoring the energy consumption in parameter update and beacon exchange, the energy consumption of a slave node consists of energy consumed by transmission (\(E_{tx}\)), data sensing (\(E_{s}\)), receiving (\(E_{rx}\)), listening (\(E_{listen}\)), and sleep (\(E_{sleep}\)). The related parameters [6] are shown in Tables 3 and 4, where the average listening current and listening time are obtained in our experiment which will be discussed in detail in the second paragraph of Section 5.2.2. Taking the sample interval as 5 minutes, we can calculate the energy consumption of a slave node in a sample interval, denoted as \(E\)  
\[E=E_{tx}+E_{s}+nE_{rx}+E_{listen}+E_{sleep} \tag{3}\]  
\[E_{listen}=I_{listen}T_{listen}V \tag{4}\]  
\[T_{listen}=t_{listen}N_{listen} \tag{5}\]  
\[E_{sleep}=I_{sleep}T_{sleep}V \tag{6}\]  
\[T_{sleep}=T-t_{tx}-t_{s}-nt_{rx}-T_{listen} \tag{7}\]  
where \(n\) is the number of neighbors; \(T\) is the sample interval and it is equal to 5 min \(\times\) 60 = 300 s; \(N_{listen}\) is the number of listening times in \(T\); \(T_{listen}\) is the total listening time in \(T\); \(T_{sleep}\) is the total sleep time in \(T\).  
\begin{table}
\begin{tabular}{|c|c|c|} \hline
**Notation** & **Parameter** & **Value** \\ \hline \(I_{sleep}\) & Sleep current (\(mA\)) & 0.03 \\ \(I_{listen}\) & Average listening current (\(mA\)) & 2.0 \\ \(V\) & Voltage & 3.0 \\ \(t_{listen}\) & Listening time (\(s\)) & 0.01 \\ \(n\) & Number of neighbors & 3 \\ \hline \end{tabular}
\end{table}
Table 4: Related parameters.  
\begin{table}
\begin{tabular}{|c|c|c|c|} \hline
**Operation** & **Energy (\(mJ\))** & **Time (s)** \\ \hline Receive a packet & 5.74704 & \(E_{rx}\) & 0.127 & \(t_{rx}\) \\ Transmit a packet & 7.66272 & \(E_{tx}\) & 0.127 & \(t_{tx}\) \\ Sense environment & 66.0 & \(E_{s}\) & 1.1 & \(t_{s}\) \\ \hline \end{tabular}
\end{table}
Table 3: Energy consumption.  
Using mode 4 of B-MAC, the default value of channel listening interval is 0.1 s, and the period of a listening is \(t_{listen}\) = 0.01 s. In five minutes, \(N_{listen}\) = 5 min \(\times\) 60/ (0.1 s + 0.01 s) = 2,727 and \(T_{listen}\) = 27.27 s, so \(E_{listen}\) = 163.6 \(mJ\). In B-MAC, a node can detect and receive data packet transmitted from its neighbors. If each of its neighbors sends a data packet, the node will receive \(n\) packets. Given \(n\) = 3, the energy consumption for receiving the \(n\) packets is 17.24 \(mJ\). \(T_{sleep}\) can be calculated as \(T_{sleep}\) = 271.12 \(s\) and \(E_{sleep}\) = 24.40 \(mJ\), so \(E\) = 278.92 \(mJ\). Using mode 4 of B-MAC, the energy consumption for listening and data receiving takes 58.6% and 6.2% of the total energy dissipation, respectively.  
While using the modified scheduling scheme, a slave node does not need to receive data packets, neither listening to the channel. The energy consumption of a slave node only consists of the energy consumption for data sampling (\(E_{s}\)), data transmission (\(E_{tx}\)), and sleep (\(E_{sleep}\)). We can calculate \(T_{sleep}\) = 298.873 s, \(E_{sleep}\) = 26.898 \(mJ\), and \(E\) = 100.5613 \(mJ\). Therefore CENet consumes about 65% less energy compared to mode 4 of B-MAC when the sample interval is 5 minutes.