## 4 Proposed Protocol
### MST and Chain Construction Period
In order to determine how many scenarios (_nscent_) are needed to run in simulation, we perform some steps as follows:

**Step 1:**: Generate randomly 50 times for 50 different scenarios with the number of sensor nodes \(N=100\) nodes in 100 \(\times\) 100 m\({}^{2}\) simulation area; in these 50 scenarios we remove the movement partly because we assume the sensor network is the stationary state after deployment. **Step 2:**: Run a simulation of LEACH-C, PEGASIS, PEGCP, and EEGT protocols on the first scenario (\(i=1\)). The simulation results are represented in the table, which \begin{table}
\begin{tabular}{c c c} \hline \hline
**No. Item** & **Parameters Description** & **Value** \\ \hline
1 & Simulation region & 100 m \(\times\) 100 m \\
2 & Number of sensing nodes & 100 nodes \\
3 & \(E_{circ}\) (Radio electric circuit energy right) & 50 nJ/bit \\
4 & \(E_{trg}\) (Radio two-ray ground energy right) & 100 pJ/bit/m\({}^{2}\) \\
5 & \(E_{stop}\) (Radio free space energy) & 0.013 pJ/bit/m\({}^{4}\) \\
6 & \(E_{DF}\) (Data fusion energy) & 5 nJ/bit \\
7 & Packet size & 1024 bytes \\
8 & Simulation time & 3600 s \\
9 & The locations of the sink & (49,175); (49,225); (49,300) \\  & _For homogeneous network model_ & \\
10 & \(E_{0}\) (Initial energy of node) & 2 J \\  & _For heterogeneous network model_ & \\
11 & \(E_{0}\) (Initial energy of node) & 1 J \\
12 & \(N_{1}\) & 0.5 \\
13 & \(N_{2}\) & 0.4 \\
14 & \(\alpha\) & 0.5 \\
15 & \(\beta\) & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The simulation parameters. indicates the proportion of alive nodes, total energy consumed, and rate of data packets received by the BS. **Step 3:**: Select performance metrics; here, we choose the energy efficiency and network lifespan metrics to evaluate. **Step 4:**: Run the next scenario (\(i=i+1\)); we present the simulation results in the table that shows the percentage of the dead nodes, total energy consumed, and amount of data packets obtained by the sink. **Step 5:**: Calculate the medium \(me_{x}\), standard deviation \(\delta\), and standard deviation ratio \(\chi\) value according to Equations (22)-(24) on the table of the simulation results. **Step 6:**: Compare the obtained results with previous ones. If the ratio of standard deviation is less than \(\chi\%\), then stop the simulation and go to Step 7, because if we run more simulations, the standard deviation ratio (\(\chi\)) will not change. Otherwise, go to **Step 4**. **Step 7:**: Graph the simulation results based on the table medium. The rate of standard deviation with the scenario \(nscen=i\) to analyze LEACH-C, PEGASIS, PEGCP, and EEGT protocol performance in terms of the percentage of alive nodes, energy consumption, and the number of data packets received by the sink with the different location according to NL. We assume the mean \(me_{i}\), standard deviation \(\delta\), and standard deviation ratio \(\chi\) can be calculated as in the equations below:

\[me_{i}=\frac{1}{nscen}\sum_{i=1}^{nscen}scen_{i} \tag{22}\]

\[\sigma_{i}=\sqrt{\frac{1}{nscen}\sum_{i=1}^{nscen}\left(me_{i}-scen_{i}\right)} \tag{23}\]

\[\chi=\sigma_{i}/max(scen_{i})\text{ with }i=1\text{ to }nscen \tag{24}\]

where \(scen_{i}\) is the simulation results of \(i\)-th scenario with LEACH-C, PEGASIS, PEGCP, and EEGT protocols. Specifically, we also run the simulation in many different scenarios for homogeneous and heterogeneous networks with the parameters given in Table 1.

### Simulation Results and Analysis

#### 5.3.1 Homogeneous Network Model

Figure 7 shows that the ratio of still-alive sensor nodes in the network (y-axis) per network lifespan depicted the number of rounds (x-axis) in LEACH-C, PEGASIS, PEGCP, and EEGT protocols with the location of the sink device at (49, 175). The red lines represent the standard deviation of the ratio of the medium (\(me_{x}\)) of EEGT protocol, with \(\chi\) deviation ratio equal to 3.9% corresponding to the number of different scenarios \(nscen=20\).