# Matching of Energy Provisions in Multihop Wireless Infra-Structures
## 5 Energy Differentiation Factor for Energy Provision in WMI Networks
### Differentiation of Energy Consumption in WMIs  
The energy consumption of a BS and the distribution of network energy consumption in WMI depend on the wireless transmitting (_TX_) and receiving (_RX_) activities of BSs. The energy consumption information that is required for efficient energy provision can be estimated based on energy consumption differentiation at each BS. This section shows how to analyze energy differentiation by estimating the traffic flow at each BS. In order to improve the accuracy of the estimate, it is necessary to consider the overhearing (_OH_) effect in the shared communication media of a WMI network. Figure 4 shows how nodes can overhear transmissions between another pair of nodes. To date, few studies have explicitly considered the _OH_ effect on energy consumption in network energy analysis.  
There are many activities associated with radio energy consumption, among which this paper focuses on the_TX_, _RX_, _OH_ data packet activities and their differentiation. This is because that _TX_, _RX_ and _OH_ are the main communication activities in wireless networks [39].  
In general, it is difficult to analyze the long-term network activities and the correlated energy consumption differences at BSs even if we know energy consumption in a single event. This section examines the energy differentiation in a WMI network based on the correlations of _TX_, _RX_ and _OH_ network activities among BSs. We introduce the line model and zone based model to quantitatively represent the energy differentiation based on the correlation of network activities in WMIs with various topologies.  
First we present an analytical framework for analysis of energy consumption at BS based on the number of _TX_, _RX_ and _OH_ operations. As shown in Table 2, we assume \(N\) is the number of BS in the network, and \(TX(i)\), \(RX(i)\), and \(OH(i)\) are respectively the number of _TX_, _RX_ and _OH_ packets in a certain time interval of duration \(T\), which increase in proportion to the value of \(T\). \(TX_{local}(i)\) is the number of packets which originate at BS(\(i\)).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline BS & \(\mathbf{TX_{local}}\) & \(\mathbf{TX}\) & \(\mathbf{RX}\) & \(\mathbf{OH}\) & \(\mathbf{E_{others}}\) & \(\mathbf{E_{c}}\) & _Diff_ \\ \hline BS(1) & \(\mathit{Src}(1)\) & \(\mathit{TX}(1)\) & \(\mathit{RX}(1)\) & \(\mathit{OH}(1)\) & \(\mathit{OH}(1)\) & \(\mathit{E_{c}}(1)\) & \(\mathit{Diff}(1)\) \\... &... &... &... &... &... &... &... \\ BS(\(i\)) & \(\mathit{Src}(i)\) & \(\mathit{TX}(i)\) & \(\mathit{RX}(i)\) & \(\mathit{OH}(i)\) & \(\mathit{OH}(i)\) & \(\mathit{E_{c}}(i)\) & \(\mathit{Diff}(i)\) \\... &... &... &... &... &... &... &... \\ BS(\(N\)) & \(\mathit{Src}(N)\) & \(\mathit{TX}(N)\) & \(\mathit{RX}(N)\) & \(\mathit{OH}(N)\) & \(\mathit{OH}(N)\) & \(\mathit{E_{c}}(N)\) & \(\mathit{Diff}(N)\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The traffic, energy consumption and differentiation at BSs.  
Figure 4: _TX-RX-OH_ interactions and energy consumption models.  
An estimate of energy consumption \(E_{c}\) of a node BS(\(i\)) can be expressed as a linear function of packet numbers as shown in Equation (5).  
\[E_{c}(i)=E_{Pt}TX(i)+E_{Pt}RX(i)+E_{Po}OH(i)+Oth(i) \tag{5}\]  
where \(E_{Pt}\), \(E_{Pt}\) and \(E_{Po}\) are the energy consumed per packet by \(TX\), \(RX\) and \(OH\) operations, and \(Oth\) represents other energy consumption that does not depend on packet number.  
\(Oth\) is assumed to be a constant times the measurement time interval.