# Reliable Link Level Routing Algorithm in Pipeline Monitoring Using Implicit Acknowledgements
## 4 Energy and Transmission Time Analysis
### Energy Consumption  
WSN nodes are composed of several functional modules that should be modeled in order to estimate the energy consumption: microprocessor, transceiver, sensor, and power supply. The most relevant is the communication model that considers the energy consumption of the transmitter and receiver [47]. Most sensor nodes support the states _ldle_, _Transmit_ and _Receive_. To model the energy consumed by transceiver, the average active ratio has been used. It is defined as the average active time divided by the total time spent [48]. It is a reasonable \begin{table}
\begin{tabular}{c c} \hline \hline
**Payload** & **Required Hops** \\ \hline
12 & 1 \\
18 & 1 \\
50 & 3 \\
102 & 6 \\
114 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of hops required to balance out a retransmission with iACK compared to eACK according to the payload size. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Intermediate Nodes** & **LWSN Length (Km)** & **eACK Delay (s)** & **iACK Delay (s)** \\ \hline
100 & 3 & 0.33441 & 0.30721 \\
1000 & 30 & 3.3441 & 3.0721 \\
2000 & 60 & 6.6882 & 6.1442 \\
3000 & 90 & 10.0323 & 9.2163 \\
4000 & 120 & 13.3764 & 12.2884 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time for end-to-end transmission with 16 bits ID. measure since energy consumption for transmission and reception (including idle listening and channel sensing) are similar in many transceivers compared to the energy consumption for standby or sleep mode [49]. An analysis has been performed to evaluate the energy consumption using iACK or eACK. Considering typical scenarios for linear structures where only alarms are transmitted, making the traffic generated very low. Let \(P_{t},~{}P_{r},~{}P_{i}\) be the power consumed during transmission, reception and idle states respectively, and let the duration of a transmission be the sum of the duration of the data frame, ACK frame, back off, IFS, turnaround, CCA and TA. When using eACK, the RXN node consumes an additional amount of energy to confirm the reception of the frame. \[AE_{\text{eACK}}=P_{r}T_{\text{ACK}} \tag{10}\]  
The percentage of additional energy consumed by the RXN node, \(\text{AE}_{\text{RXN}}\), using eACK to receive the frame, transmit the ACK and be ready to retransmit the frame, can be calculated as, (Equation (11)):  
\[AE_{RXN}=\frac{P_{t}T_{\text{ACK}}}{P_{r}T_{fra}+P_{t}T_{\text{ACK}+}P_{i}(T_{ TA}+T_{BO}+T_{\text{CCA}})} \tag{11}\]  
The energy consumed in the TXN node to know that the frame sent was received can be calculated for the eACK (Equation (12)) and iACK schemes (Equation (13)):  
\[E_{eACK}=P_{t}T_{fra}(x)+P_{r}T_{\text{ACK}}+P_{i}(T_{IFS}+T_{TA}+T_{BO}+T_{CCA}) \tag{12}\]  
\[E_{\text{iACK}}=P_{t}T_{fra}(x)+P_{i}(T_{TA}+T_{BO}+T_{CCA}) \tag{13}\]  
The percentage of additional energy consumed by the TXN node, \(AE_{TXN}\), using eACK to send the next frame, can be calculated as Equation (14):  
\[AE_{TXN}=\frac{P_{r}T_{ACK}+P_{i}((T_{ruaite}-T_{ruait})~{}+2T_{TA}+T_{BO}+T_{ CCA})}{P_{t}T_{fra}+P_{r}T_{ACK+}P_{i}(T_{ruaite}~{}+4T_{TA}+T_{BO}+T_{ BO1}+2T_{CCA}} \tag{14}\]  
The percentage of additional energy consumed by the TXN node, \(AE_{TXNf}\) using eACK to retransmit the frame that did not reach the RXN node, can be calculated as Equation (15):  
\[AE_{TXNf}=\frac{P_{t}(T_{ruaite}-T_{wait})}{P_{t}T_{frame}+P_{i}(T_{ruaite}~{} +2T_{TA}+T_{BO0}+T_{CCA})} \tag{15}\]  
Many research works have evaluated sensor node energy consumption while transmitting, receiving, or idle. In most cases energy consumption is similar in transmission or reception mode (processing and waiting) [50; 51] and slightly larger than the idle mode consumption. In our experiments, and according to the specifications of our hardware [52], our node uses 55.8 mW, 49.9 mW, and 12.3 mW for \(P_{t}\), \(P_{r}\), and \(P_{i}\) respectively, in non-beacon mode. In all cases, these values depend on the particular sensor node. Figure 15 shows how energy consumption in the TXN and RXN nodes is reduced when iACK is used in comparison with eACK.