## 2 Proposed Routing Scheme
### The Routing Scheme
#### 2.2.2 Steady Phase
The performance evaluation was based on the following performance metrics as used in [21; 35]. Note that the efficiency is multi-dimensional and may be determined by each of the following parameters. 1. Number of alive nodes per cluster round. It indicates the number of nodes alive from the network for every cluster round, and this depends on the availability of energy remaining in the network. A routing algorithm is more efficient if it can keep several nodes alive after many routing rounds. 2. Number of dead nodes per cluster round. As a result of changing energy, it levels inside the network during network survival time. This also indicates the possible lifetime remaining of the network. A routing scheme is more efficient if it reduces the number of dead nodes in each cluster. * Throughput. It means the numbers of packets sent to the BS by the nodes in each round. The throughput really shows the effective energy utilization corresponding to the underlying routing algorithm. * Packets received. indicates the actual packets acknowledged by BS. A routing scheme is more efficient if it maximizes the number of delivered packets to the destination (base station in our case). * The residual energy of the network. It helps to analyze the energy consumption of nodes in each round. In many cases, a routing algorithm which ensures less energy consumption is considered to be more efficient. For balancing the energy in the network, clustering has been applied in many rounds to update the routing tree. For each round, the value of each of the above parameters is calculated. The network lifetime is studied and results are presented in Figure 2. The figure shows the number of active sensors for each clustering round in SEP, MGEAR, and the proposed routing protocol HMGEAR. The figure shows that, in HMGEAR, all the 100 nodes stayed alive longer than both SEP and MGEAR and hence have a better lifetime than the two protocols. The figure also shows that the number of alive nodes per round, in the case of HMGEAR, decreases slowly compared to the two other protocols and converges to zero the last. This confirms the fact that for each round it is safest to use HMGEAR. \begin{table}
\begin{tabular}{c l} \hline \hline
**Parameters** & **Values** \\ \hline Network field & \(100\,\mathrm{m}\times 100\,\mathrm{m}\) \\ \hline Number of nodes & 100 \\ \hline Initial energy of normal nodes (\(E_{0}\)) & 0.5 J \\ \hline Message size & 4000 bits \\ \hline \(E_{elc}\) & 50 Nj/bit \\ \hline \(E_{fs}\) & 10 Nj/bit/m\({}^{2}\) \\ \hline \(E_{mp}\) & 0.0013 Pj/bit/m\({}^{2}\) \\ \hline \(P_{opt}\) & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 2: Number of alive nodes per round. Figure 6 shows the leftover energy of the sensors per round in all the schemes. Initial energy values are different for considered schemes due to the difference in energy optimization parameters used in each protocol and the distance of the Base station from the deployment area (50 m, 200 m). In the proposed protocol, the Base station is far away from the field, but heterogeneous nodes (nodes with the highest energy than homogeneous), gateway nodes, and energetic heads were used. In MGEAR, only homogeneous nodes and gateway were used. In the SEP scheme, although only the heads are heterogeneous, its network was originally designed with the Base station at the center and closer to the nodes. However, positioning the Base station outside and also far away from the field compelled it to have the highest energy consumption rate, and that makes its residual energy reach zero within that shortest possible time. It can be noticed that the rate of energy depletion in the proposed scheme is lower than the existing algorithms. This reflects the energy-conserving mechanisms that were introduced and implemented in the new scheme which includes selecting heads using residual energy of the nodes, the multi-hop communication technique employed, and implementation of energy hole removing technique.