## 4 System Model
### Energy Consumption Estimation of Mobile Nodes  
The energy consumption of nodes plays a significant role in the selection of robust and qualified intermediate nodes, which collaborate to improve the overall network performance. The mobile nodesin the MANETs are battery operated and their energy is limited. Therefore, battery life of the nodes should be taken into account while selecting a set of intermediate nodes for route establishment to a destination in the network. Moreover, the mobile nodes operate in four states, which are; transmission, receiving, idle, and sleep states. The energy consumption in idle and sleep states is low; hence, the transmission and receiving states of nodes are considered in the design of the routing algorithm of our proposed scheme. In the proposed scheme, the energy of each node is linearly discharged as a function of current load based on the Coulomb counting technique [56], which accumulates the dissipated Coulombs from the beginning of the discharge cycle. It estimates the residual energy based on the difference between the accumulated value and prerecorded full charge value of the battery capacity. The proposed scheme utilizes a generic radio energy model [57] to estimate the consumed energy for each state of node such as (\(E_{Initial}^{i}(t)\), \(E_{Residual}^{i}\), \(E_{Consumption}^{i}\) and \(E_{operation}^{i}(t)\)). Energy consumption in different states of nodes and duration of time in each state of nodes, affect the performance for the proposed routing scheme. The initial energy level of the intermediate node \(i\) at the time \(t\) is denoted by \(E_{Initial}^{i}(t)\) and the residual energy \(E_{Residual}^{i}(t+\tau)\) of node \(i\) at the period of time \(\tau\) is calculated as follows:  
\[E_{Residual}^{i}(t+\tau)=E_{Initial}^{i}(t)-E_{Consumption}^{i}(t+\tau) \tag{1}\]  
where \(E_{Consumption}^{i}(t+\tau)\) refers to the energy consumption of node \(i\) for a period of \(\tau\), which is the energy consumed during transmission, receiving, exchanging routing information control packets, and during internal operation time of nodes. In the proposed scheme, energy consumption is estimated based on the circuitry power consumption, number of packets exchanged, and time spent in each state. Thus, the energy consumption in a transmission state of the node \(i\) for transmitting \(n\) number packets can be calculated as follows:  
\[E_{Transmission}^{i}(t+\tau)=n\times P_{Transmission}^{i}(t+\tau) \tag{2}\]  
whereas \(P_{Transmission}^{i}(t+\tau)\) denotes the amount of power consumed during transmission of \(n\) number of data packets and exchanging routing information control packets with neighbor's nodes at the period of \(\tau\) time, the unit is in Watts per second. Similarly, the energy consumed by node \(i\) during the receiving state for transmitting \(m\) numbers of packets and including control packets at the period \(\tau\) is calculated as follows:  
\[E_{Recieve}^{i}(t+\tau)=m\times P_{Recieve}^{i}(t+\tau) \tag{3}\]  
where \(P_{Recieve}^{i}(t+\tau)\) represents power consumed by node \(i\) during exchange control messages and receiving \(m\) number of packets at a time \(\tau\). Moreover, all the nodes consume energy when they perform internal operation such as connecting, managing, catching, and updating database at the time of \(\tau\) period, which is denoted by \(E_{operation}^{i}(t+\tau)\).