## 4 Proposed Scheme
### New Node-Association  
Once the CHs are declared, they forward the CH-Announcement messages in their vicinity. The CH-Announcement message is comprised of all the relevant information such as residual energy, computation capability, traffic load, and distance from CH to the sink node. A child node may receive multiple CH-Announcement messages from multiple CH nodes in the range. Therefore, child node associate itself with the CH which has high residual energy, high computational capability, low traffic load, less distance between CH and sink node and less distance between itself and CH. The rationale behind the consideration of such a large number of parameters for CH selection is to enhance the lifetime of CH in case of application scenarios which generates a massive volume of data. Besides, the CHs are not frequently changed which reduces the control overhead that occurs because of the frequent re-clustering process. Figure 2 illustrates the node association process where the node \"U\" receives CH-Announcement message from two CHs (i.e., CH1 and CH2). Node \"U\" has to decide its association with the best CH among CH1 and CH2. Based on the available resources of CH1 and CH2, the node \"U\" executes new Node-Association process and decides the best CH to join. Let us suppose the CH1 has higher amount of resources than other. CH1 is considered as the best CH for the node \"U\" to associate with. Therefore, the node \"U\" sends a Node-Association message to CH1 and associates itself with it. Initially on receiving CH-Announcement messages from several CHs, the child node(s) calculates Euclidean distance from CH which is defined as follows:  
\[d(n,CH)\ =\ \sqrt{\left(x-a\right)^{2}+\left(y-b\right)^{2}} \tag{3}\]  
where \(d(n,CH)\) is the distance between CH and a child node (n), \(x\), and \(y\) are the location coordinates of the child node (\(n\)) and \(a\), and \(b\) are the location coordinates of CH. After calculating distance, the child node selects the preeminent CH based on a multi-criteria decision-making technique known as TOPSIS [34; 35; 36]. The rationale of using a multi-criteria decision-making process is that it allows the node to select the best CH among several potential CHs in its range based on non-homogeneous parameters and the step-wise detailed description of the process by adopting TOPSIS is expressed as follows. 1. Decision Matrix Development Consider a child node having \"_m_\" CHs in its range. The child node organizes the CHs attributes in a decision matrix (\(X\)) as defined in Equation (4). \[X=\ \left( \begin{array}{cccc}X_{(1,1)}&X_{(1,2)}&X_{(1,3)}&.&X_{(1,n)}\\ X_{(2,1)}&X_{(2,2)}&X_{(2,3)}&.&X_{(2,n)}\\.&.&.&.&.\\.&.&.&.&.\\ X_{(m,1)}&X_{(m,2)}&X_{(m,3)}&.&X_{(m,n)}\end{array} \right)\] (4) where \(X_{m,n}\) is the value of \(n\)th resource criteria of \(m\)th CH, \(m\) represents the total number of CHs, and \(n\) is the total number of the resource criteria such as residual energy, computation capability, traffic load, distance from CH to the sink node, and distance from the child node itself to the CH. Figure 2: Nodes association process. 2. Resource Criteria Normalization The values of all these criteria do not lie in the same range (e.g., the value of residual energy is not equal to available storage), therefore, the resource criteria must have to be normalized to a common range in order to fairly select the CH. The normalized form of the decision matrix is obtained by employing Equation (5) and is defined as follows: \[{X^{*}}_{(i,j)}=\frac{X_{(i,j)}}{\sqrt{\sum_{j=1}^{n}X_{(i,j)}^{2}}}\textit{ where }i=1...m,j=1...n\] (5) \[X^{*}=\left( \begin{array}{cccccc}X^{*}{}_{(1,1)}&X^{*}{}_{(1,2)}&X^{*}{}_{( 1,3)}&.&.&X^{*}{}_{(1,n)}\\ X^{*}{}_{(2,1)}&X^{*}{}_{(2,2)}&X^{*}{}_{(2,3)}&.&.&X^{*}{}_{(2,n)}\\.&.&.&.&.&.\\.&.&.&.&.\\.&.&.&.&.\\ X^{*}{}_{(m,1)}&{a^{*}}_{(m,2)}&{X^{*}}_{(m,3)}&.&.&{X^{*}}_{(m,n)}\end{array} \right)\] (6) The normalized decision matrix, \(X^{*}\) is obtained using Equation (6). 3.