# Multi-Path Data Distribution Mechanism Based on RPL for Energy Consumption and Time Delay
## 3 Adaptive Multipath Traffic Loading Based on RPL, AMTL-RPL
### Energy Balance Based on the RPL
#### 3.1.2 The Metric Definition of Energy Balance  
The amount of data transmission plays an important role for the whole network's transmission rate. Even given global information, choosing an optimized energy balance algorithm is still challenging. This paper uses a multipath to balance the overload of the network's traffic. According to RPL protocol, once DODAG has been constructed, all the traffic would transmit through one path until the network topology changes. To ensure the maximum network lifetime, we need to improve DODAG, which means making a multi-path available. One node could distribute traffic to multiple parent nodes instead of the preferred one. This ensures that all of parents can be energy balanced. We distribute data among different parent nodes to make sure that the overload of the residual energy of the subsequent bottleneck nodes becomes balanced. In this paper, we consider the time that the first node takes to run out of energy as the whole network's lifetime. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Notation** & **Meaning** & **Notation** & **Meaning** \\ \hline \(E_{txt}(x)\) & Sending energy consumption of \(x\) & \(T_{r}\) & Receive time \\ \hline \(E_{rec}(x)\) & Receiving energy consumption of \(x\) & \(E_{ort}\) & Current energy \\ \hline \(E_{cmp}(x)\) & Calculating energy consumption of \(x\) & \(E_{res}\) & Residual energy \\ \hline \(E_{t}\) & Sending energy consumption per second & _Tat(x,y)_ & Data transfer from \(x\) to \(y\) \\ \hline \(E_{r}\) & Receiving energy consumption per second & _Buffer\_Use(x)_ & Node x cache usage \\ \hline \(E_{c}\) & Energy consumption per instruction cycle & \(N_{unk}\) & \begin{tabular}{c} Task processing \\ instruction cycle \\ \end{tabular} \\ \hline \(D_{d}\) & Sending rate & \(D_{p}\) & Processing rate \\ \hline \(D_{r}\) & Receiving rate & \(PRR(x\),y) & \
\begin{tabular}{c} \(x\) received a number of \\ ACK packets \\ \end{tabular} \\ \hline \(S_{r}\) & Receive data & \(T_{p}\) &
\begin{tabular}{c} Processing time of each \\ instruction \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notation used in the article. In fact, bottleneck nodes will consume energy no matter which node we choose as the preferred parent. In order to ensure a more efficient evaluation of whether the bottleneck node is energy-balancing, it is necessary to evaluate the degree of dispersion of the remaining energy consumption of these nodes. Based on the relevant mathematical knowledge, we use range, average deviation, and standard deviation to assess the degree of data dispersion. Nevertheless, through many tests, we found that these metrics could not embody the distribution of the remaining energy consumption of the bottleneck nodes. To estimate the distribution of the energy consumption of the bottleneck nodes precisely, this paper provides the measurement of the energy distribution equilibrium degree based on [PERSON]'s evaluation model Pareto (1958). The definition of the energy of dispersion: Assume the rational number set represents sensor energy, \(a_{i}\geq 0\), and the ED (energy of dispersion) criteria can be:  
\[ED=\sum_{i=1}^{n}\varpi_{i}\cdot{a_{i}}^{2} \tag{5}\]  
Here, \(\varpi_{i}=\frac{1/(a_{i}-E(A))^{2}}{1/D(A)}\), \(D(A)=\left\|A-E(A)\right\|_{2}/n\), \(E(A)=\left\|A\right\|_{1}/n\), \(\left\|\cdot\right\|_{x}\) represents the norm of \(x\). To validate the effectiveness of ED, we compare some typical measurements for evaluating the dispersion degree, including the range, average deviation and standard deviation. Firstly, we demonstrate numerical evaluations to compare their differences. A total of 200 numbers from 1 to 100 were randomly selected, and these measure values were calculated individually. The test was run 1000 times and recorded the maximum value, the minimum value and the average value. The result can be seen in Table 2 and Figure 4.  
The above table shows that the ED can express the data dispersion degree quite well and reflects the fluctuation degree more clearly.