# 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
: _The HCD guarantees the load balancing of CHs in intracluster and intercluster multihop routing._

**Proof of Lemma 4. ** According to the Equation (4), it can be demonstrated that the node radius depends on its distance to the BS and its remaining energy. Therefore, CHs having more distance to BS and higher remaining energy make larger clusters and they have more CMs. Hence, it consumes more energy to receive and collect data from CMs. Moreover, ACH nodes are applied to maximize the stability and balanced energy consumption of CMs during data transmission to the CH and also to balance CH energy consumption for receiving the data. On the other hand, CHs close to the BS with less energy have a smaller radius and less CMs. Therefore, they save more energy for receiving and collecting data from the CMs, and they guarantee the load balancing of the HCD protocol. \(\square\)

## 5 Simulation Results

The main purpose of this research was to reduce energy consumption and increase the network life time. In order to achieve this purpose, simulations were performed in MATLAB programming environment. Furthermore, to evaluate network stability, efficiency, and throughput of the proposed algorithm, this algorithm was compared to ECDC (2013) [24], HUCL (2015) [15], and EADUC-II (2016) [25] algorithms. ### Simulation Scenarios

We also performed simulations for two different states shown in Table 2. In the first scenario, there are 100 nodes in 200 \(\times\) 200 spaces and the BS is located outside the network space and located at 100 \(\times\) 250. In the second scenario, the location of the BS has changed to the network center and 100 \(\times\) 100 location. In the proposed algorithm the count of alive nodes, the average of network energy and network stability, first node death (FND), half node death (HND), death of 10% and 20% of nodes (PND), and last node death (LND) during the whole simulation time were evaluated. The simulation was performed in 50 periods. Definitions of some important concepts:

* Network lifetime: the time interval from the start of network operations to LND. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network** & **BS** & **Number of Node** & **Network Space** \\ \hline scenarios \#1 & (100,250) & 100 & 200 \(\times\) 200 \\ scenarios \#2 & (100,100) & 100 & 200 \(\times\) 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Scenarios. * Network stability: the time interval from the start of the network operations to FND. * Throughput or efficiency: the number of data packets sent by a network to the BS. Efficiency improvement has a direct co-relation with increased network stability and the network lifetime. * Load balancing: traffic load distribution. Its advantage is that when the load is well-distributed throughout the nodes, it results in balanced energy consumption. It also prevents the sudden death of the nodes caused by overusing them and increases the network stability. ### Simulation Parameters

Simulation parameters are displayed in Table 3. The optimum values of some of the parameters (for example \(RL_{max}\)) were determined from various simulation results. We performed simulations several times to determine the round numbers in a major slot (Figure 2) and major slot in data transmission stage (Figure 2). Simulation parameters, such as the nodes locations, are considered to be the same for all the nodes so that the results are reliable and solid. This simulation plays a crucial role in the proposed protocol. In this protocol, by decreasing the number of rounds, we can more accurately simulate a dynamic method which results in increased overhead and energy consumption and declined the network life span. In contrast, by increasing the number of rounds the proposed protocol gets closer to the static methods and, therefore, leads to a decrease is overhead and loss of energy in CH and, subsequently, the stability and throughput of the network reduced.