## 4 Simulation and Analysis  
### Simulation Setup  
To simulate the proposed protocol, the weighted probabilities for the nodes have been chosen based on the pre-processing of sensor nodes' energy patterns and observing various parameters based on the narrations in [3; 12]. Initially, a 2D virtual field, (\(x\)-\(y\)), is created with \(500\times 500\) the unit dimension. A total of 500 nodes were assumed with the base station or sink node in the middle of the experimental virtual field. Table 2 shows the additional parameter list used for simulation. The parameter values in Table 2 were taken from [3; 12]. Tables 1 and 2 illustrate the standard value to be considered for a sensor node inspired by the capacity and capability of actual sensors. These parameters helped to formulate the concept and establish a simulation environment. These standard parameters are treated as constant values of literals used in the program. The energy dissipated by the associated Cluster Head [22] is  
\[E_{elec}=E_{Tx}=E_{Rx} \tag{9}\]  
An innovative approach is considered for election probabilities of normal, intermediate, and advanced nodes [16]. The election probability for normal nodes is chosen to be  
\[P_{norm}=\frac{P_{opt}}{1+a\times m+b\times x+ab\times z} \tag{10}\]  
The election probability for intermediate nodes is chosen to be  
\[P_{int}=\frac{P_{opt}\times(1+b)}{1+a\times m+b\times x+ab\times z} \tag{11}\]  
The election probability for advanced-intermediate nodes is chosen to be  
\[P_{ad-int}=\frac{P_{opt}\times(1+ab)}{1+a\times m+b\times x+ab\times z} \tag{12}\]  
The election probability for advance nodes is chosen to be  
\[P_{adv}=\frac{P_{opt}\times(1+a)}{1+a\times m+b\times x+ab\times z} \tag{13}\]  
In this approach, additional parameter \(z\) is the percentage of the advance-intermediate nodes and \(ab\) is the percentage increment in the energy of the advanced-intermediate nodes with respect to normal nodes. It is observed that using the additional advanced-intermediate nodes may end up slightly reducing the network lifetime, although it may give better energy response. Therefore, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbolic Significance** & **Value** \\ \hline Sink Node Coordinates & \((X_{sn},Y_{sn})\) & \((250,250)\) \\ No. of Nodes & Nodes or n & 500 \\ Initial Energy & \(E_{0}\) & 0.5 J \\ Transmission Power & \(E_{T_{x}}\) & \(5\times 10^{-8}\) J \\ Received Energy & \(E_{R_{x}}\) & \(5\times 10^{-8}\) J \\ Data Aggregation Energy & \(E_{DA}\) & \(5\times 10^{-9}\) J \\ Max. Rounds & rmax & 3000 \\ Packet Size & Packet & 4000 bits \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Additional simulation parameters for the multi-tier structureto improve the life of the network, some modifications have been made at the network initialization level. The basic network energy distribution model used in simulations is shown in Figure 6.  
In terms of this model, it has been analyzed for the energies of Virtual WSN nodes using the proposed simulation. The result of the simulation is a node energy distribution histogram plot as shown in Figure 7. This depicts the variation of the residual energy of the entire WSN after the death of the first node (assuming 100% remaining residual energy just after the FND). This graph has three axes. Axis-A shows percentage loss of data/message throughout the WSN (as once nodes start dying, and data could not be collected/transmitted from the node). The blue histogram region is accompanied to axes A and C (Interpret Graph from right to left). Axis B shows the residual energy remaining in the network that is accompanied by the orange line. Axis-C shows the percentage of dead nodes. The linearity of this graph shows that the number of dead nodes is inversely proportional to the residual energy of the system. This means that WSN in the simulation is balanced, which is not the case in DEC and MDEC.