## 4 Proposed Protocol
### MST and Chain Construction Period
After we process the simulation from Step 2 to Step 7 as in Section 5.2, we have selected the medium value and standard deviation ratio after running 20 different scenarios applied with EEGT protocol (\(t_{round}=10\), EE = 1041 (Kbytes/Joule), \(\chi=1.0\%\), and \(1\%\) dead node = 829 th round); with the LEACH-C protocol, the number of processed different scenarios is \(nscen=19\), and (\(t_{round}=10\), EE = 610 (Kbytes/Joule), \(\chi=2.5\%\), and \(1\%\) dead node = 478 th round); with the PEGASIS protocol, the number of processed different scenarios is \(nscen=20\), and (\(t_{round}=10\), EE = 657 (Kbytes/Joule), \(\chi=2.5\%\), and \(1\%\) dead node = 631 st round); and with the PEGCP protocol, the number of executed different scenarios is \(nscen=20\), and (\(t_{round}=20\), EE = 1020 (Kbytes/Joule), \(\chi=7.6\%\), and \(1\%\) dead node = 539 th round). Normally, if \(t_{round}\) increases, throughput and energy efficiency will also increase, but the \(1\%\) dead node will be earlier in all four protocols. However, for the LEACH-C protocol, when \(t_{round}=300\), EE = 120 (Kbytes/Joule), CHNs die too early, so the collected information of the whole cluster is not sent to the sink device. In most cases, our proposed EEGT protocol still achieves better energy efficiency than the three conventional protocols in changing the size of rounds, and the most suitable of our proposal EEGT is EE = 1108 (Kbytes/Joule) and \(1\%\) dead node = 877 th round when \(t_{round}=50\) s.

#### 5.3.2 Heterogeneous Network Model

In this research, we have implemented a \(50\%\)_normal_ node, \(30\%\)_advanced_ node, and \(20\%\)_super_ node for a heterogeneous network model. The energy level of the _advanced_ node and the _super_ node is initialed 1.5 and 3 times greater than the _normal_ node (initial energy of _normal_ node \(E_{0}=1\)oule), respectively. As presented in Equation (1), we establish the total energy initial \(E_{init}=\)155 Joules for all nodes, in which \(NN=50\)_normal_ sensor nodes; \(NA=30\)_advanced_ nodes; and \(NS=20\)_super_ nodes. The simulation parameters are configured for discussed all protocols, as shown in Table 1. In order to evaluate the performance of EEGT, we also perform the simulation from Step 2 to Step 7 as in Section 5.2; the simulation results are graphed in the figures following after we calculated the medium value and standard deviation ratio. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Protocols**} & \multirow{2}{*}{**Rounds**} & \multicolumn{8}{c}{**The Percentage of Dead Nodes**} \\  & & **EE (Kbytes/Joule)** & **1\%** & **10\%** & **25\%** & **50\%** & **75\%** & **95\%** & **100\%** \\  & (s) & **(\%\%)** & **(\%\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline \multirow{8}{*}{LEACH-C, [21]} & 10 & 610(2.5) & 478(14.3) & 603(12.3) & 685(2.9) & 762(2.9) & 857(2.6) & 988(5) & 1140(7.8) \\  & 50 & 720(2.5) & 34(14.4) & 178(21.4) & 442(9.7



As shown in Figure 11, we can see that the ratio of alive nodes decreases along the network lifespan (number of rounds) in the heterogeneous network. By considering the residual energy factor of the nodes in the CHNs decision, the EEGT improves the performance of the network compared with LEACH-C, PEGASIS, and PEGCP in terms of energy consumption balance and the 1% node death even though the PEGCP achieves the last node death longer than three others protocols due to unbalanced energy consumption. Figure 12 depicts the total energy consumption of smart micro-sensor nodes in Joules during the network lifespan (rounds) in a heterogeneous network with four protocols. Based on the simulation results, we obtain the value at that time of the standard deviation ratio \(\chi=4.9\%\); \(\mathit{nscen}=19\) different scenarios with LEACH-C; \(\chi=4.1\%\), \(\mathit{nscen}=19\) different scenarios with PEGASIS; \(\chi=2.3\%\); \(\mathit{nscen}=19\) different scenarios with EEGT protocols.