## 5 Simulation Results  
We assume that the service area of a Wi-Fi sensor network is circular, that an AP is located at the center of the service area, and \(l\) = 10, 20, 30, \(\ldots\) 100, 200, 400, 600, 800, or 1000 Wi-Fi sensors are associated with the AP and randomly located in the circular service area. Many smart factories have over 1000 sensors for the realization of IoT technology [40; 41]. To cover this number of sensors by sensor networks, each sensor network should interconnect with up to 1000 sensors. The radius of the service area is denoted by \(r\), and the transmission range of each Wi-Fi sensor, for which the radius \(R\) = \(r\), 1.1\(r\), 1.2\(r\), 1.3\(r\), 1.4\(r\), or 1.5\(r\), is assumed to be circular. The simulation parameters for the number of sensors in the sensor network, and the transmission range of each sensor, their values, and other details of simulation setup are presented in Table 2. Three sample Wi-Fi sensor networks with \(l\) = 10, 20, and 30 Wi-Fi sensors and \(R\) = \(r\) are generated to closely observe the behavior of the proposed node insertion algorithm, as shown in Figures 5-7. Applying the proposed node insertion algorithm to the three sample networks in Figures 5-7, serially connected multipolling sequences are constructed for the Wi-Fi sensors, and each constructed serially connected multipolling sequence is presented using a connected arrow. Figure 4: Process of selecting next nodes in node insertion algorithm. Figure 5: Sample Wi-Fi sensor network and formations of serially connected multipolling sequences with \(l=10\) and \(R=r\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of Sensors (\(l\)) & 10, 20, 30,..., 100, 200, 400, 600, 800, 1000 \\ Transmission Range (\(R\)) & \(r\), 1.1\(r\), 12\(r\), 1.3\(r\), 1.4\(r\), 1.5\(r\) \\ Shape of Service Area & Circular \\ Location of AP & Center of Service Area \\ Location of Sensors & Uniformly Randomized \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters, values and details of simulation setup. In Figures 5-7, the coordinate value (0, 0) is the center of the circular service area, and the other coordinate values are relative to the radius \(r\) of the service area. Since the coordinate value of the location of each sensor and the transmission range (\(R\)) are relative to the radius \(r\) of the service area, that is, the coordinate value of the location of each sensor and the transmission range are simultaneously proportional to the radius \(r\) of the service area, the value of \(r>0\) does not affect the operation of the proposed node insertion algorithm or the simulation results. As shown in Figures 5-7, two serially connected multipolling sequences for each sample network with 10 and 20 Wi-Fi sensor nodes were derived, and only a single serially connected multipolling sequence for the sample network with 30 Wi-Fi sensor nodes was derived using the proposed node insertion algorithm. It can be seen that the algorithm tries its best not to skip the nodes simultaneously connected from the most recently added nodes in the sequences from the behavior of the proposed node insertion algorithm for sequencing nodes to construct serially connected multipolling sequences. Figure 6: Sample Wi-Fi sensor network and formations of serially connected multipolling sequences with \(l=20\) and \(R=r\). We generated 50 random networks to obtain the performance of the proposed node insertion algorithm for the mean number of serially connected multipolling sequences for Wi-Fi sensor networks for each combined case of \(l=10\), \(20\), \(30\), \(\ldots\), \(100\), \(200\), \(400\), \(600\), \(800\), or \(1000\) Wi-Fi sensors, and \(R=r\), \(1.1r\), \(1.2r\), \(1.3r\), \(1.4r\) or \(1.5r\).