# A Routing Protocol for Multisink Wireless Sensor Networks in Underground Coalmine Tunnels
## 6 Evaluation of Algorithm Performance
### Power Efficiency  
It is extremely difficult (and almost impossible) to change the battery of the sensor nodes in the coalmine tunnel, and thus the power efficiency needs to be optimal to ensure that the network lifetime is prolonged. The power efficiency is defined in this section as follows: the sensor nodes in the network reach the sink nodes through one hop or two hops, and the communication radius of each sink is also controlled to obtain the optimal transmission power, which thus minimizes the total energy consumption used from all the sensor nodes to the sink. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Network coverage & (0, 0)–(1000, 20) m \\ Number of sink nodes & 1–12 \\ \(n\) & 200 \\ Initial energy of sensor node & 0.5 J \\ \(\varepsilon_{\text{mp}}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ \(E_{DF}\) & 5 nJ/bit/signal \\ \(\varepsilon_{\text{fs}}\) & 10 pJ/bit/m\({}^{2}\) \\ \(E_{\text{elec}}\) & 50 nJ/bit \\ \(t_{0}\) & 4 s \\ Data grouping & 512 bit \\ \(g_{t}\) & 25 dBi \\ \(S^{r}\) & 25 dBi \\ \(\lambda\) & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. If we suppose that \(k\) sinks are present in the network, then the total transmission power, \(P_{sum}\), of the sink nodes in the network is expressed as Equation (18), according to the relationship between the transmission and receiving power and the communication distance described in Equation (4),  
\[P_{sum}=\sum_{i=1}^{k}P_{t,i}=\sum_{i=1}^{k}\frac{P_{r,i}d_{i}^{2}}{\varphi}. \tag{18}\]  
For the hardware energy consumption of the radio, the energy consumption of the transmitter at the time of transmission includes the wireless electronic device and the power amplifier, and the energy consumption of the receiver at the time of reception is only that of a radio electronic device. The first-order radio energy consumption model proposed in [35; 36; 37; 38; 39] is used in our study; the model considers both the transmitting energy and receiving energy consumption. Based on this model, the energy consumed by the data transmission of _lbit_ to \(s\) is shown as follows,  
\[E_{Tx}\left(l,s\right)=\left\{ \begin{array}{l}lE_{elce}+l\varepsilon_{fs} \varsigma^{2},s<s_{0}\\ lE_{elce}+l\varepsilon_{mp}s^{4},s\geq s_{0}\end{array} \right., \tag{19}\]  
where \(E_{elce}\) refers to the energy consumed by the transmitting circuit. The free space model is adopted if the transmission distance is less than the threshold value, \(s_{0}\); otherwise, the multipath attenuation model is used. The value of \(s_{0}\) is 75 m according to [33]. \(E_{fs}\) and \(\varepsilon_{mp}\) refer to the energy required by the two models for power amplification. The energy that the sensor node consumes for receiving _lbit_ is calculated as follows,  
\[E_{Rx}\left(l\right)=lE_{elce}. \tag{20}\]  
In addition, \(E_{DF}\) is used to represent the energy used for fusing the unit bit data in this study. The sensor nodes need to receive the broadcast packets from the sink and to send data to the cluster head node or sink; therefore, the total energy consumption can be expressed by the following equation,  
\[E_{total}=E_{Tx}\left(l,s\right)+E_{Rx}\left(l\right)+lE_{DF}=\left\{ \begin{array}{l}lE_{elce}+l\varepsilon_{fs}\varsigma^{2}+lE_{elce}+lE_{DF}+ \mathrm{E}_{x},s<75\\ lE_{elce}+l\varepsilon_{mp}s^{4}+lE_{elce}+lE_{DF}+\mathrm{E}_{x},s\geq 75\end{array} \right. \tag{21}\]  
in which \(E_{x}\) is a fuzzy factor. The actual roadway environment is not fully adapted to the first-order radio energy consumption model; however, as the haulage roadway is a horizontal tunnel for transport and ventilation, its conditions are much better and thus closer to this model. We use the fuzzy factor to make adjustments, with the aim of ensuring the experiment can meet the requirements of the model. From Equation (21), we can see that if we want to reduce the total energy consumption of the sensor nodes, we need not only to consider the process of transmitting data, but also the process of receiving data.