## 3 Proposed Techniques
### Initial Phase
#### 3.1.2 Independent Nodes (INs)
* Intra-clusters RoutingAt the beginning of each round, the Ns of the second level in each cluster arrange their RTs based on a cost function that is comprised of two parts: the first part is related to the relative location of the next hop node (NHN) to the CH, while the second part is allocated for the ratio of the residual energy in the NHN. The cost value can be computed using the following equation [12]:

\[C_{NHN}(i)=C_{NHN-CH}(i)+\alpha\cdot C_{NHNE}(i) \tag{8}\]

The \(C_{NHN-CH}\) parameter refers to the distance cost for the NHN. The \(C_{NHNE}\) parameter indicates the energy cost for the NHN. The variable \(i\) indicates the member's number within the set of nodes, which the source node (SN) selected and added to its RT in the current round. Finally, the \(\alpha\) parameter represents the relative weight of the energy cost part in the cost equation. The first part can be obtained using Equation (9) [12]:

\[C_{NHN-CH}(i)=\frac{{D_{i}}^{2}}{{SN_{D-CH}-NHN_{iD-CH}}} \tag{9}\]

The \(D_{i}\) parameter indicates the distance from the SN to NHN. The \(SN_{D-CH}\) parameter refers to the distance between the SN and its CH, while \(NHN_{iD-CH}\) indicates the distance between the NHN and its CH. The second part of the cost function is the energy ratio in the NHN and it can be computed using Equation (10):

\[Energy\ ratio\ =\ \frac{{RE_{NHN}}}{{IE_{NHN}}} \tag{10}\]

The \(RE_{NHN}\) parameter refers to the residual energy in NHN, whereas the \(IE_{NHN}\) indicates the initial energy of NHN. The proposed approach allocates a cost value for every ratio of energy. Figure 7 shows an example of this assumption. Distinctly, for the highest energy ratios have been given the lowest cost values, especially the ratio values that exceed 50% of the initial energy. After calculating the cost values for all the available routes, the N arranges them in its RTs. Thus, the route, which has the lowest cost value is chosen to be used at the beginning of the round. During the round, the Ns of the first level broadcast periodically updated messages in order to update RTs of Ns, which exist in the second level. Based on the updated messages, the Ns update their RTs. Hence, the routes cost values will be dynamically modified. As a result, the route, which was initially selected, may change. Figure 7: An example of the energy costs for the N, CH, and IN. Inter-clusters Routing

The dynamic approach is also used for routing out of the clusters. Accordingly, all the CHs and INs try organizing their \(RT\)s. For this reason, they compute the costs for all available routes, which are announced among each other. The cost function comprises of two parts: the first part refers to the cost of the relative position of the next hop (NHI), which might be a CH or IN, to the BS. The second part of the cost function is allocated for the energy cost for the NHI. Thus, the cost value can be calculated using Equation (11) [12]:

\[C_{NHI}(n)=C_{NHI-BS}(n)+\alpha\cdot C_{NHIE}(n) \tag{11}\]

The \(C_{NHI-BS}\) parameter refers to the distance cost for the NHI. The \(C_{NHIE}\) parameter indicates the energy cost for the NHI. The variable \(n\) indicates the members of the group of INs and CHs, which have been selected by the source of the data (SNI), either CH or IN, as NHIs in the current round. The first part of the cost function can be calculated using Equation (12) [12]:

Figure 2:0

Here, the \(D_{n}\) indicates the distance from the SNI to the NHI, whereas the \(SNI_{D-BS}\) and \(NHI_{D-BS}\) parameters denote the distance from the SNI and NHI to the BS, respectively. In the second part, an energy cost is given for every remaining energy ratio in NHI. Thus, every energy ratio is replaced with a cost value. Figure 7 shows an example of the energy cost values for the CHs and INs. The higher energy ratios are given lower energy costs, particularly when the energy ratio is overridden 50%. For reducing the energy load on the CHs, it is noticed that the energy ratios of the INs are granted lower cost values in comparison with the CHs.