## 4 Proposed Protocol
### MST and Chain Construction Period
As shown in Figure 12, it is evident that the energy consumption of the network increases drastically when the network lifespan increases. However, our proposed EEGT protocol has the lowest energy consumption compared with the other three popular protocols due to reducing communication distance in the data transmission routes to the sink device. Figure 13 is a reverse representation of Figure 10 about the percentage of dead nodes in the heterogeneous network, which shows 5%, 10%, 25%, 50%, 75%, 95%, and 100% node death. The EEGT protocol improved the network lifespan by decreasing the ratio of dead nodes from 5% to 95% in comparison with the existing protocols such as LEACH-C, PEGASIS, and PEGCP. However, PEGCP has a longer network lifespan at 100% node death because PEGCP unbalances energy consumption among nodes in the network. \[me_{i}=\frac{1}{nscen}\sum_{i=1}^{nscen}scen_{i} \tag{22}\]0 The ratio of the number of alive sensors per round in heterogeneous network. \[me_{i}=\frac{1}{nscen}\sum_{i=1}^{nscen}scen_{i} \tag{22}\]1 Total energy consumption by sensors in a heterogeneous network. Figure 14 presents the ratio of data packets the sink device receives when its location is varied. This is also an important performance measurement for estimating the energy efficiency utilization of routing protocols because the more efficiently it uses in the network, the more data packets are received in the sink device. The ratio of the data packet received by EEGT attained about 95% with the average of the standard deviation ratio obtaining \(\chi\) by approximately 3.0% in the 19 different scenarios, which are also higher than those of LEACH-C, PEGASIS, and PEGCP, with about 30% with \(\chi\) by approximately 1.9% in 17 different scenarios; 20% with \(\chi\) by approximate 4.6% in 18 different scenarios; and 5% with \(\chi\) by approximately 1.8% in 19 different scenarios, respectively. This is because our proposed protocol can calculate suitable time duration during the steady data transmission phase for each round so that the EEGT protocol achieves greater energy efficiency and longer network lifespan in both heterogeneous and homogeneous network models. \[me_{i}=\frac{1}{nscen}\sum_{i=1}^{nscen}scen_{i} \tag{22}\]2 The ratio of data packets received at the sink device with different locations of it in a heterogeneous network. \[me_{i}=\frac{1}{nscen}\sum_{i=1}^{nscen}scen_{i} \tag{22}\]3 The ratio of dead sensors per network lifespan (rounds) in a heterogeneous network. Furthermore, Table 3 presents the energy efficiency and the percentage of dead nodes in the FDD, HDD, and LDD for LEACH-C, PEGASIS, PEGCP, and EEGT with changing \(t_{round}\) from 10 to 700 s of the heterogeneous network model. We can see in Table 3 that the EEGT protocol achieves better energy efficiency than that of the three existing protocols because the energy consumed for data transmission paths based on MST and chain is lower than in a single hop due to the distances among connected nodes being smaller. Specifically, the energy efficiency of our proposed EEGT protocol at \(t_{round}=50\) s is EE = 1091 (Kbytes/Joule), \(\chi=2.4\%\), 1% node death = 485 th round, while LEACH-C, PEGASIS, and PEGCP protocols only achieve EE = 852 (Kbytes/Joule), \(\chi=2.3\%\), 1% node death = 43 rd round, EE = 849 (Kbytes/Joule), \(\chi=4.2\%\), 1% node death = 117 th round, and EE = 1069 (Kbytes/Joule), \(\chi=9.9\%\), and 1% node death = 349 th round, respectively. This improvement is because our proposed method divides the sensing field into cells and the selecting CHNs, which have high residual energy and are near the sink device, to become super-CHNs. Moreover, EEGT establishes communication routes inter-cellularly based on the ant colony algorithm to reduce overall the distance communication from CHNs to the sink device. As a result, our protocol improves the network lifespan. ## 6 Conclusions

Because of sensor nodes' restricted battery energy resources, energy saving is the principal objective when designing routing protocols for WSNs [32].