## 3 Evaluation
### Experiment Design  
The proposed algorithm is analyzed on a wireless sensor network deployed within a square field of 100 \(\times\) 100 m\({}^{2}\). The number of nodes for all the experiments is 250, which are randomly distributed within the area following a uniform distribution. All the nodes and the BS remain static for the whole network lifetime, and the batteries of the nodes are never charged or replaced. The remaining setup parameters are as follows: the initial energy of all the nodes is 0.5 J, the length of the control messages is 200 bits, and the length of data messages is 2000 bits. All those setup parameters are summarized in Table 4.  
To evaluate the proposal with different and realistic configurations of WSNs, the BS is placed in three different locations that constitute the three different scenarios to test (see Figure 5):  
* Scenario 1. The BS is at one corner of the square field at coordinates (100,0) meters. * Scenario 2. The BS is far and outside the sensing area at coordinates (150,50) meters. * Scenario 3. The BS is at the center of the deployment field at coordinates (50,50) meters. The values for the variables of the energy model, which are the same for all scenarios, are found in Table 5: \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Deployment field & 100 \(\times\) 100 m\({}^{2}\) \\ Nodes deployed & 250 \\ Initial energy of nodes & 0.5 J \\ Length of control message & 200 bits \\ Length of data message & 2000 bits \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experiment setup parameters. Figure 5: Deployment field for the scenarios used in the experiments. Our proposal, named Distributed Clustering Algorithm Guided by Base Station (DCAGBS), is compared with four other proposals widely used in the research literature:  
* Low-Energy Adaptive Clustering Hierarchy (LEACH) [5]. It is a distributed algorithm based on a pure stochastic CH selection method which is used like a reference in most clustering proposals. The parameter \(p\) of this algorithm is set to 0.05 in our simulations. * Cluster-Head Election using Fuzzy logic for wireless sensor networks (CHEF) [17]. CHEF is a centralized method that decides the best CH based on an expert system. The fuzzy system has three input variables: energy, concentration, and centrality of nodes. * Energy-Efficient Distributed Clustering algorithm based on a Fuzzy approach with non-uniform distribution (EEDCF) [34]. EEDCF is a distributed algorithm based on fuzzy logic. The inputs are energy, the number of neighbor nodes, and the energy of those nodes. This method has a phase in which different nodes compete to be CH. The node with the best fuzzy output becomes the CH eventually. * Enhanced Unequal Distributed Type-2 Fuzzy Clustering algorithm (EUDFC) [23]. EUDFC is an interval Type-2 fuzzy distributed system. The system variables are energy, distance to the BS, the average of the distances of the nodes that join a CH, and the number of rounds that a node is only a sensor. EUDFC has a competition phase in which only \(np\) CHs is chosen, where \(n\) is the number of nodes in the system. In addition to the reference clustering algorithm LEACH, the other algorithms represent illustrative examples of fuzzy-logic based clustering algorithms with a centralized approach (CHEF) and two distributed implementations based on Type-1 and Type-2 Interval Fuzzy systems (EEDCF and EUDFC, respectively). To test the performance of DCAGBS and the other four methods, they have been evaluated with simulations for the three scenarios. Hence, each scenario has been simulated 30 times with different random node locations to make the results statistically significant. The results obtained from the average of those simulations for each scenario are three metrics widely used in wireless sensor networks: (i) round at which the First, Node Dies (FND), (ii) round at which Half of the Nodes have Died (HND), and (iii) round at which the Last Node Dies (LND).