## 5 Simulation and Performance Evaluation  
The RSC algorithm was implemented using MATLAB 2013a and core i5 processor with Windows-7. The transmission radius of the sensor nodes was at 100 m.  
The experiment results were taken from twenty different scenarios like varying the number of nodes from 500 to 1000. The network field was assumed to be a virtual circular-shaped area where sensor nodes were distributed randomly. The number of nodes deployed and the number of rounds were changed frequently to obtain the cluster data for further analysis. The sink node was placed in the center of the circular area initially. The sink node location was changed randomly in different scenarios. The parameters used in MATLAB are defined in Table 1.  
The cluster head selection in RSC is presented as an example scenario in Figure 2. The radius of the inner circle was twice that of the remaining circles to avoid the hotspot issue since all the communications were towards the sink location. The angle \(\theta\) was taken as 90\(\circ\) for fixing the quadrant in this example scenario, hence \(n\) was 4 and each quadrant was taken as a single sector. Subsequently, the second layer was subdivided into three sectors by \(\frac{\pi}{3}\). Furthermore, the next layer was subdivided into five sectors by \(\frac{\pi}{5}\) for the third circle, and so on. The nodes were thrown randomly in the deployment area and each sector was considered as a cluster. Each cluster needed a CH to aggregate the data.  
The CH was identified by the minimum distance closest to the midpoint of the cluster, as shown in [PERSON] et al. [17; 18]. Initially, the sink was located at the center of the network field, and then it was changed dynamically to evaluate the performance.  
The process of routing takes place when the node forwards the data collected towards its CH. The probability of data transmitting to the nearest CH towards the sink node is a binomial polynomial problem. Angular inclination routing is one of the alternatives to ensure that the data can be reached to the Sink node.  
The CH transmitted the data towards the subsequent lower layer sensing node in the angular inclination routing, as discussed in [23; 30]. This process continued toward the angle of the sink node until the data reached the sink node. The scenario presented in Figure 3 shows that the third layer of the CH wanted to transmit the data to the sink. The sink location was identified and a virtual path was framed from CH to the sink with 30-degree angular inclination. In this routing, the number of hops was greatly reduced and there was a moderate increase in the transmission range.  
\begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Parameters Used**} & \multicolumn{1}{c}{**Values**} \\ \hline Area of deployment (x,y) & 500 m + 500 m \\ Number of nodes & 1000 \\ Coordinate of the sink node (\(S_{x}\), \(S_{y}\)) & (260, 260) m \\ The initial energy of each sensor & 2 j (Joule) \\ \(E_{elc}\) & 50 nJ/bit \\ \(\varepsilon_{fs}\) & 10 pJ/bits/m\({}^{2}\)) \\ \(\varepsilon_{mp}\) & 0.0013 pJ/bits/m\({}^{4}\)) \\ \(E_{DA}\) & 5 nJ/(bit * signal) \\ \(\delta_{0}\) & \(\sqrt{\frac{\varepsilon_{fs}}{\varepsilon_{mp}}}\) \\ x,y coordinates of midpoint of grid & \(S\big{(}p_{x},p_{y}\big{)}\) \\ x,y coordinates of all nodes & \(A(x,y)\) \\ Number of rounds \(K\) & 500 \\ Control packet size \(P_{ctrl}\) & 200 bits \\ Data packet size \(P_{data}\) & 3000 bits \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters used in RSC.  
Figure 2: Node deployment and CH selection.