## 6 Discussion  
Generally, when an existing connectivity-based multipolling mechanism based on the TSP model is applied to derive the optimal number of serially connected multipolling sequences for wireless LANs, the number of searches required by the existing connectivity-based multipolling mechanism increases as the number of nodes increases in wireless LANs [1; 2; 3; 4]. Specifically, through simulation experiments conducted over more than 1000 random networks with \(l\) = 1000 sensors and transmission range \(R\) = \(r\), 1.1\(r\), 1.2\(r\), 1.3\(r\), 1.4\(r\) or 1.5\(r\), the search algorithm based on the TSP model was found to take on average more than 14.67 s to derive the optimal number of multipolling sequences for each network and to take more than ten minutes to derive the optimal number of multipolling sequences in some cases of networks. A new node insertion algorithm is proposed to resolve the issue of excessive time taken by the existing connectivity-based multipolling mechanism in which the search space for the optimal number of serially connected multipolling sequences is dramatically reduced such that the number of real-time derived serially connected multipolling sequences converges to only one as the number of sensors in Wi-Fi sensor networks increases. When the number of sensors in Wi-Fi sensor networks is equal to 1000, the mean numbers of serially connected multipolling sequences are equal to 1.06, 1.2, 1.08, 1.18, 1.06, and 1.12 for \(R\) = \(r\), 1.1\(r\), 1.2\(r\), 1.3\(r\), 1.4\(r\) and 1.5\(r\), respectively, according to the simulation experiments in Section 5. The strong result--that in real time, almost only one serially connected multipolling sequence can be derived for a Wi-Fi sensor network with many sensors--makes the MAC protocol based on the connectivity-based multipolling mechanism more attractive for Wi-Fi sensor networks.  
From Figure 4, it can be seen that as new nodes are selected, _depth_ does not decrease, which provides a clue for further reducing the search space. The proposed node insertion  
Figure 9: Results of considered mean numbers of previous nodes.  
algorithm was found to be more efficiently implemented using one or more additional techniques for reducing the search space, such that serially connected multipolling sequences could be derived within approximately 15 ms for each simulated case in Section 5. A subsequent paper will be prepared and submitted for publication for a detailed implementation of techniques to reduce the search space further.  
Now, why only one serially connected multipolling sequence can exist for the connectivity-based multipolling mechanism in a Wi-Fi sensor network with many sensors is discussed. The connectivity-based multipolling mechanism is based on the connectivity among nodes in wireless LANs. The connectivity-based multipolling mechanism aims to find the minimal number of serially connected multipolling sequences that cover all the nodes in wireless LANs. The performance of the search algorithm for the minimal number of serially connected multipolling sequences, which is the number of derived serially connected multipolling sequences, depends heavily on the connectivity of the set of nodes of the sensor network. Fortunately, generally, an exponentially increasing connectivity for the set of nodes in the sensor network is found as the number of nodes increases in the sensor network. The exponentially increasing connectivity ultimately leads to only one serially connected multipolling sequence as the number of nodes increases in the sensor network.