# A Hybrid Unequal Clustering Based on Density with Energy Conservation in Wireless Nodes
## 3 The Proposed HCD Algorithm
### Protocol Performance
#### 3.2.1 Cluster Initialization
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Protocol**} & **FND (100 Nodes)** & **10\% PND (90 Nodes)** & **20\% PND (80 Nodes)** & **HND (50 Nodes)** & **LND (0 Nodes)** \\ \cline{2-10}  & **Time** & **Packets** & **Time** & **Packets** & **Time** & **Packets** & **Time** & **Packets** \\ \hline ECDC & 345.2 & 34515 & 569.1 & 56204 & 644.9 & 62693 & 743.5 & 6900.7 & 1283.6 & 7620.3 \\ HUCL & 205.2 & 20518 & 489.8 & 47679 & 617.4 & 58584 & 736.8 & 66323 & 856.9 & 68948 \\ EADUC-II & 358.1 & 35808 & 590.5 & 58125 & 667.9 & 65680 & 712.4 & 67864 & 742.5 & 68265 \\
**HCD** & **863.5** & **86348** & **966.7** & **96087** & **983.4** & **97222** & **1013.6** & **98538** & **1088.3** & **99168** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results of stability period and lifetime for scenario 2. ### The Average of the Energy of Alive Nodes

As it was assumed, the network is formed by heterogeneous nodes which have an energy between 0.5 to 1.5 \(j\). Figure 12 illustrate the energy consumption of each node in the proposed algorithm and in scenario 1. Figures 12 and 13 compare the amount of energy in each node in HCD for scenarios 1 and 2, at the beginning of the network and during the rounds 250, 500, and 750. The proposed protocol has excellent load balancing. At first, due to the assumption of heterogeneous nodes, an energy difference between the nodes is observed. However, gradually in a period of 250, and particularly 500, during the performance of our proposed protocol, it can be seen that the energy difference between nodes is reduced. This indicates that in the proposed protocol we have high load balancing. The proposed protocol is able to distribute the energy consumption between all nodes and pave the way for increasing the load balancing by selecting the proper CH. In addition, by determining the suitable CH, the presented protocol divided the energy consumption among nodes and it helped reducing energy consumption by multihop transmission. In this type of transmission distance is short, and hence, less energy is required for transmission. Accordingly, the presented protocol prevented the immediate reduction of energy in nodes by selecting appropriate CH and avoiding direct transmission to distant nodes. Consequently, the close and distant nodes consumed energy in a balanced way, the stability was increased and the throughput was improved. Figure 11: The average of the number of alive nodes for scenario 2. Figure 10: The average of the number of alive nodes for scenario 1. One of the important reasons in the proposed protocol which contributed to the increased network lifetime is that it omitted the maximum control messages in the network. Figures 14 and 15 show the energy consumption for control messages in the proposed protocol and other protocols. The proposed protocol decrease energy consumption in terms of control messages to 300% in comparison to EDCD and EADUC-II and 100% in comparison to HUCL. Figure 12: Energy consumption of HCD for scenario 1. Figure 13: Energy consumption of HCD for scenario 2. Given that in our proposed protocol there were 6 rounds of data transmission per each major slot without the overhead control message, and since the protocol had 42 rounds of data transmission to the BS per each transmission stage, this protocol was able to optimize the energy consumption by reducing the overhead. This led to an increase in average energy of nodes. Figures 16 and 17 show the average energy of alive nodes during the simulation. Figure 16: The average energy of alive nodes for scenario 1. Figure 14: Total energy consumption for control message in scenario 1. Figure 15: Total energy consumption for control message in scenario 2. According to the results, it can be concluded that in the proposed method by reducing the network overhead, the energy consumption has been reduced. ### Throughput

Figures 18 and 19 demonstrate packet production in relation to the round indicating an increased efficiency of the proposed protocols.