## 3 Heterogeneous Network Model of the Proposed Models
### Iterative Solver with Min-Cost Optimization  
Iterative reconfigurations are required to save energy resources because sensor nodes have limited battery capacity and tend to leave the network operations once their batteries have drained out. Hence, the key is to rotate the operational responsibilities equally, so that the SDN central controller monitors the resources carefully and develops an intelligent iterative reconfiguration mechanism distributed along time periods \(t\), where \(t=1,2,\ldots,T\) with \(T>1\). One time iteration length can be decided by the network administrator according to the remaining network resources, and the SDN central controller can reprogram sensor nodes dynamically on the network operation. This multiple time period network reconfiguration mechanism is defined as a 0-1 integer programming model. In the following, we concentrate on developing a realistic mechanism to achieve this performance optimization task.  
The proposed protocols develop the cluster-based organization of sensor nodes and FECHs effectively communicate with the central controller of SDN. Therefore, an undirected graph \(G=(C,R,rE_{C})\) represents the clustering network model of WSNs at the infrastructure layer; where \(C\) defines the set of FECHs decided by the SDN controller, \(R\) represents the existing links \(r=i,j\), configuring the available FECHs \(i,jeC\), and \(rE_{C}\) is the representation of residual energy resources. Every single link \(reR\) occupies the traffic capacity of \(\alpha_{r}\) and has a cost of \(\beta_{r}\); this as a whole defines the  
Figure 4: Iterative clustering topology in the case of the SAMCFIR routing protocol.  
Figure 5: Application-sensitive environmental reporting of the SACFIR routing protocol.  
Figure 6: Application-sensitive environmental reporting of the SAMCFIR routing protocol.  
maximum amount of the flow roundtable for the current configuration settings, while the system has to bear the communication cost paid per unit of routed flow, respectively.  
If a sensor node has a sensed value, it initializes a unicast demand of \(ueU\) and a link with destination pair \((S_{u},D_{u})eC^{2}\). The set \(U\) represents the active demands on this current network configuration and utilizes specific resources to route reports through the network. The SDN central controller needs to provide the most economical pathway to solve an evolving instance of the Minimum Cost Function (MCF) problem, which can be formulated at a given time as the linear program (1)-(3); where real variables \((X_{p})peP\), \((Y_{r})reR\) and \((Z_{e})eerE_{C}\) represent the path, link and residual energy utilization and take values in the range \([0,1]\). The minimum cost function can then be expressed using the above-defined notations:  
\[Min-cost^{OPT}(X_{p},Y_{r},rE_{e})=min\sum_{t=1}^{T}\sum_{reR}Y_{r}\beta_{r} \tag{7}\]  
\[s.t.\sum_{t=1}^{T}\sum_{peP_{u}}X_{p}=1 \tag{8}\]  
\[s.t.\sum_{t=1}^{T}\sum_{eerE_{u}}Z_{e}=1 \tag{9}\]  
\[\sum_{t=1}^{T}\sum_{ueU}\sum_{peP_{r}=ueP_{r}}X_{p}\Gamma_{u}\leq Y_{r}\alpha_ {r} \tag{10}\]  
The objective function (1) models the overall price paid for using the network links, and the constraints (2) ensure that the entire demand \(\Gamma_{u}\) is routed through a set of paths with routing splits \(X_{p}\Gamma_{u}\). Similarly, the constraints (3) are the residual energy constraints, and (4) are the link capacity constraints.