## 2 Proposed Routing Scheme
### The Routing Scheme
#### 2.2.2 Steady Phase
The proposed scheme achieves all these successes while remaining the most energy efficient for all the rounds. Figure 5: Packets received by the BS per round. Figure 6: Residual energy per round. It is important to note that the number of alive nodes in the network remains highest for the proposed routing algorithm, while the number of dead nodes remains least for all routing rounds. On the other hand, the number of packets sent and received to the base station is always (for all routing rounds) highest for the proposed routing scheme when compared with MGEAR and SEP. The proposed model achieves these mentioned qualities while nodes in the network retain the most potential (i.e., are more energetic) when compared to the two algorithms. ## 4 Conclusions

In this paper, a heterogeneous MGEAR routing protocol, HGEAR, has been proposed to act as a remedy to the shortcomings of traditional MGEAR Protocol. The new scheme solved the problem of using a probabilistic approach in selecting cluster heads. This was achieved by introducing the residual energy heads selection approach. The approach has ensured that nodes with higher residual energy are selected as the heads and are able to effectively transmit data to the Base station. The new algorithm also introduced heterogeneous nodes in the regions that are far from the Base station as well as employing multi-hop communication technique among nodes in all the regions. This has reduced the energy depletion of distant nodes as they transmit their reports to the Base station as shown in Figure 4. The scheme further implements an energy hole removal mechanism to prevent holes that may be created as a result death of nodes. With this, nodes transmit their data based on a certain energy threshold below that which they can transmit. This has reduced the death rate of nodes, as shown in Figure 3. Each energy-saving technique that has been introduced in this scheme has resulted in low energy consumption, as indicated in Figure 6. A simulation was conducted, and results showed that the new protocol performed better than the existing schemes in respect to stability period, throughputs, residual energy, and network lifespan. **Author Contributions:** Conceptualization, F.J. and E.T. ; Formal analysis, F.J., E.T. and M.I.D. ; Funding acquisition, E.T. ; Investigation, F.J.; Methodology, F.J.; Resources, M.I.D. ; Software, F.J.; Validation, F.J. and E.T. ; Visualization, F.J. and E.T. ; Writing--original draft, F.J.; Writing--review & editing, E.T. and M.I.D. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable

**Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. ## References

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