# An Energy-Saving Forwarding Mechanism Based on Clustering for Opportunistic Networks
## 3 Energy Impact
\[y=q_{0}+q_{A}{}^{x}{}_{A}+q_{B}{}^{x}{}_{B}+q_{C}{}^{x}{}_{C}+q_{D}{}^{x}{}_{D }+q_{AB}{}^{x}{}^{x}{}_{A}{}^{x}{}_{B}+q_{AC}{}^{x}{}^{x}{}_{A}{}^{C}+\ldots+q_{ BC}{}^{x}{}^{x}{}^{x}{}_{B}{}^{x}{}_{C}+\ldots+q_{ABCD}{}^{x}{}^{x}{}^{x}{}_{B}{}^{x}{}^{x}{}_{D} \tag{1}\]  
In order to find out the effect of each factor (explained in Table 3) on the response of interest y, one can assign minimum and maximum levels to the selected factors (see [PERSON]'s book [PERSON] (2018) for more details) and record the result of the probability of delivery of the message obtained by simulation. We determined the density of the scenario as a factor to analyze how scenarios can affect the simulation results. We defined two battery ranges, so the values represent which battery level node keeps cooperating in the network and carrying messages from other nodes. In the experiment's execution, we used an epidemic routing algorithm. In the minimum value (between 75% and 100%), nodes cooperate only if their battery levels are in this range (low cooperation). In the maximum value of (0% the 100%), nodes carry messages from other nodes regardless of their remaining energy level (high cooperation). Since the scenario needs to be similar to the real-world ones, we chose a sparse (Reality) and a dense (Infocom), extracting information from real experiments. In Section 5.1, we present further details for the selected scenarios. Table 3 presents the investigation of the effect of the node's battery charge level on the message's probability of delivery and the levels attributed to each factor in the simulation. The minimum and maximum levels are assigned to variables of set X = {x1, x2, x3, x4}, which alternate their levels according to Table 3. For example, x2 = \(-1\) is assigned to battery range = [75, 100] and x2 = 1 is assigned to battery range = [0, 100]. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Factor** & **Minimum Value (\(-1\))** & **Maximum Value (\(1\))** \\ \hline x1—Scenario density & Reality & Infocom \\ x2—Battery range & 75, 100 & 0, 100 \\ x3—Buffer size & 10 M & 100 M \\ x4—Message generation & 600, 3600 & 100, 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Factors of experiments. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**\#** & **x1** & **x2** & **x3** & **x4** & \(y\) \\ \hline
1 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & 0.0246 \\
2 & \(-1\) & \(-1\) & \(-1\) & \(1\) & 0.2308 \\
3 & \(-1\) & \(-1\) & \(1\) & \(-1\) & 0.4757 \\
4 & \(-1\) & \(-1\) & \(1\) & \(1\) & 0.856 \\
5 & \(-1\) & \(1\) & \(-1\) & \(-1\) & 0.035 \\
6 & \(-1\) & \(1\) & \(-1\) & \(1\) & 0.0682 \\
7 & \(-1\) & \(1\) & \(1\) & \(-1\) & 0.5025 \\
8 & \(-1\) & \(1\) & \(1\) & \(1\) & 0.8496 \\
9 & \(1\) & \(-1\) & \(-1\) & \(-1\) & 0.0382 \\
10 & \(1\) & \(-1\) & \(-1\) & \(1\) & 0.2308 \\
11 & \(1\) & \(-1\) & \(1\) & \(-1\) & 0.4641 \\
12 & \(1\) & \(-1\) & \(1\) & \(1\) & 0.8596 \\
13 & \(1\) & \(1\) & \(-1\) & \(-1\) & 0.0259 \\
14 & \(1\) & \(1\) & \(-1\) & \(1\) & 0.2393 \\
15 & \(1\) & \(1\) & \(1\) & \(-1\) & 0.4719 \\
16 & \(1\) & \(1\) & \(1\) & \(1\) & 0.9029 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variation of Xi vs. result of variable \(y\). The next step is to calculate the percentage of message delivery variance attributed to each of the four factors and each interaction between them. The percentage of variation captures the importance of each factor in the response variable. Table 4 describes the percentage of variation pointed out by the factorial design. The battery range factor has a more significant impact on the message's probability of delivery (76.96%). The scenario and the joining factor composed of both battery range and scenario explain 18% and 3% of the variation. Thus, the remaining node energy necessary to cooperate is the most significant factor that deserves further analysis.