# Enhanced Three Layer Hybrid Clustering Mechanism for Energy Efficient Routing in IoT
## 4 Network Model of ETLHCM  
In this paper, first order radio model is adapted from [28]. It is used to calculate the energy that is consumed in transmitting (\(E_{TX}\)) and receiving (\(E_{RX}\)) of packets size \(l\) bits over distance \(d\) by each deployed sensor node in the network. \[E_{TX}=\left\{ \begin{array}{ll}l*(E_{elc}+\varepsilon_{fs}*d^{2}),&d<d_{0}\\ l*(E_{elc}+\varepsilon_{mp}*d^{4}),&d\geq d_{0}\end{array} \right. \tag{1}\]  
Distance threshold \(d_{0}\) is the normal transmission range of sensor node, \(E_{elc}\) and \(\varepsilon_{fs}\) are the energy dissipation to run the radio and free space model of transmitter amplifier and their values are 50 nJ/bit and 10 pJ/bit/m\({}^{2}\) respectively. \(l\) is the data packet size and \(\varepsilon_{mp}\) is the multi path model of transmitter amplifier and its value is 0.0013 pJ/bit/m\({}^{4}\). The receiving energy \(E_{RX}\) can be calculated as:  
\[E_{RX}=l*E_{elc} \tag{2}\]  
Figure 2 explains the aforementioned (\(E_{TX}\)) and (\(E_{RX}\)) consumption process in first order radio model [28]. It is assumed in this paper that all sensor nodes are randomly deployed in the field of fixed dimension. The deployed sensor nodes are homogenous and all have same capabilities and limited power source of same initial energy that cannot be recharged or replaced. The sink node is assumed to have no energy constraints and is deployed outside the coverage area. All sensor nodes are assumed to know about the location of the sink node and are able to find their own location information after deployment. Sensor nodes are static and do not change their locations once they are deployed. Sensor nodes determine the distances between each other based upon the received signal strength. In the initial round, all deployed sensor nodes transmit their location and energy information hop by hop to sink. Sensor nodes join grid or upper layer in the same mechanism as explained in [9]. Nodes which are selected as grid head broadcast their assigned role, and pause the sensing role. Other sensor nodes, after joining upper layer, start the exchange of control packets between each other for cluster head or lower layer head selection. All sensor nodes share their residual energy and location information via control packet. Fuzzification process of shared parameters by sensor nodes takes place distributively. The node of higher residual energy and lower Euclidean distance to both sink and grid  
Figure 2: Energy consumption in transmitting and receiving data packet in first order radio model. head is chosen to be cluster head. The euclidean distance between any two sensor nodes \(a\) and \(b\) is calculated from the following two dimension euclidean distance Equation (3). \[d(a,b)=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}} \tag{3}\]  
where \(x_{1}\) and \(x_{2}\) are the width dimensions, \(y_{1}\) and \(y_{2}\) are length dimensions of sensor nodes \(a\) and \(b\) respectively. Nodes with CH role collect data from sensor nodes, compress it, and transmit it toward GH, which in turn forward them toward sink, while the rest of the sensor nodes sense the environment, collect data, and transmit it to their CH. Unlike HHCA and other previous three layer routing techniques, sensor nodes are not required to repeat the cluster head selection process and exchange of control packets between each other after every round. In the proposed mechanism, the main goal is to minimize the wasteful operations in every round and save nodes energy. Equation (4) shows the objective function of the proposed mechanism. \[Min\sum_{r=1}^{r=max}WE_{consumed}(r)\forall r\in R \tag{4}\]  
\(WE_{consumed}\) is calculated using Equation (5). \[WE_{consumed}=\sum_{i=1}^{N}d_{o}(i)\times(E_{TX}ControlPacket+E_{RX}ControlPacket) \tag{5}\]  
where \(WE_{consumed}\) is the amount of energy consumed per round in the exchange of control packets between all deployed sensor nodes \(N\) for CHs selection. \(d_{o}\) is the maximum distance between two neighboring sensor nodes.