## 2 Cluster Head Selection
### Self-Organized Schemes
#### 2.1.2.1 Energy Expenditure  
The node selected as CH consumes more energy than other nodes within the network and demise of a CH leads up to losing all the data of an area monitored by its cluster member nodes. Therefore, selection of the nodes having the highest remaining energy as CH is quite desirable [13; 14; 15; 16; 17]. Considering a ratio of the current level to the initial energy level of the node as a coefficient of the probability equation of the threshold value T(n) is proposed in [14; 23]. The nodes with higher level of remaining energy have more chance to be selected as CH. However, the average energy of the nodes decreases after certain number of rounds. Therefore, multiplying T(n) with a small fraction lessens the chance of nodes to be selected as CH and may lead to the rounds with few or even no CHs, although there are still nodes available having enough battery power to communicate with the BS and are able to play the CH role. The possible solution for the issue is proposed in [14] by normalizing the energy coefficient, presented in Equation (2):  
\[ \begin{split}\mathrm{T}^{\prime}(\mathrm{n})=\left\{\!\!\!\!\! \frac{P_{CH}}{1-\ P_{CH}*\left(r_{c}\bmod\frac{1}{P_{CH}}\right)}\!\!\!\!\!\! \left[\frac{E_{c}}{E_{i}}+\left(r_{c}\operatorname{div}\frac{1}{P_{CH}} \right)\left(1-\frac{E_{c}}{E_{m}}\right)\right],\text{if}\ n\in G\\ 0,\text{otherwise}\end{split} \right.\end{split} \tag{2}\]  
where \(E_{c}\) is the current energy and \(E_{i}\) is the initial energy of node \(n\). When \(r\) reaches the value _1/P_ the threshold _T(n)_ is reset to the value it had before the inclusion of the remaining energy into the threshold-equation. Hence, by decreasing the average energy level of the nodes, the chance being a CH is not eliminated  
In [13], the paper proposes a modified version of threshold equation for CH selection based on the square of the ratio of the current to the initial level of energy of the nodes. According to the Equation (3), when the node \(n\) has more energy, the influence of the energy ratio is relatively large, and by depleting the battery power of the node, the effects of the energy ratio factor are diminished too. Therefore, the proposed scheme also mitigates the problem of decrease in the probability chance of individuals by depletion of their battery power:\[T^{\prime}(n)=\frac{p_{CH}}{1-p_{CH}*(r_{c}mod1/p_{CH})}*\sqrt{\frac{E_{c}}{E_{i}}} \tag{3}\]  
The scheme presented in [16], in addition to the current energy level of the nodes, considers three other factors in the last round including the initial energy level, the total dissipated energy level of a node and the initial average remaining energy level of all the nodes within the cluster. In other words, the main idea of the algorithm is to choose nodes with higher energy level and lower energy dissipation as CHs. Based on Equation (4), nodes having the energy level lower than the average energy level of the cluster and even nodes with higher energy level but consuming relatively more energy in the last round have lower chances to be selected as CH. Adding the dissipated energy of the nodes in last round can further regulate the variation speed of T'(n):  
\[T^{\prime}(n)=\frac{p_{CH}}{1-p_{CH}*\left((r+1)mod\frac{1}{p_{CH}}\right)}[ \frac{E_{r}-E_{r,disstpate}}{E_{r,average}-E_{r,disstpate}}] \tag{4}\]  
where E\({}_{r}\) is the node residual energy in the beginning of the last round \(r\), \(E_{r,\_average}\) is the average initial energy of all nodes within the cluster in the last round \(r\) and \(E_{r,\_dissipate}\) is the node total dissipated energy for data transmission during last round \(r\). Cluster-Chain Routing Protocol (CCRP), proposed in [15], uses an additional factor of the number of the neighbours to increase the chance of the nodes having more neighbours as being CH. Thus, the algorithm limits the intra-cluster communication cost of cluster members with the CH:  
\[\text{T'(n)}=\left\{