# A Lifetime Maximization Relay Selection Scheme in Wireless Body Area Networks
## 6 Performance Evaluation
### Result Analysis
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Nodes** & **Enumeration** & **The Rapid Solution** \\ \hline
6 & 0.008530s & 0.000010s \\
8 & 0.084878s & 0.000016s \\
10 & 0.834952s & 0.000017s \\
12 & 7.510353s & 0.000025s \\
16 & 104.487781s & 0.000028s \\
20 & 6532.097615s & 0.000039s \\ \hline \hline \end{tabular} The hardware settings for implementing the simulation in this paper: CPU i-7 2600 3.4 GHz; Memory 8 G RAM.  
\end{table} 
Table 3: Time complexity of the algorithms. Figure 2: Convergency loop performance comparison. In addition, the optimal value obtained from the optimization using enumeration is also presented in the comparison in order to show the performance gap between the proposed solution and the optimal value. Figure 3 shows the lifetime performance of each algorithm with the variation of \(\sigma^{2}\). The larger the value of \(\sigma^{2}\) is, the more serious the energy inequality in the network that exists. The lifetime on the \(y\)-axis in the unit of superframes represents how many superframes the network gets through before the first sensor node runs out of energy under different relay selection algorithms. That is to say, more superframes means longer lifetime of the network. It can be firstly seen from the figure that the performance of the rapid solution is very close to the optimal value of the optimization. Precisely, the performance gap between the proposed heuristic solution and the optimal value of the optimization is only about 0.5% on average. Combining with the time complexity analysis in Table 3 and Figure 2, it can be inferred that the proposed heuristic iteration described in Algorithm 1 is an effective and time-efficient solution to the optimization problem. In addition, it is confirmed that, throughout the simulations in this paper, performance gap between the rapid solution and the optimal value of the optimization is always very small similar with the results shown in Figure 2. Hence, for simple and clear illustration in the following performance analysis, we will use the results obtained from the rapid solution to represent the performance of LMRSS. It can be obviously seen from Figure 3 that LMRSS is always the better relay selection scheme in terms of lifetime performance no matter how \(\sigma^{2}\) varies compared with the benchmark, sum-rate algorithm and max-rate algorithm. Furthermore, it could be found that with the increasing value of \(\sigma^{2}\), the advantages of Rapid MRS over these three algorithms become larger. When \(\sigma^{2}=0\), which means that residual energy is all equal to 2 J, the lifetime performance of the proposed algorithm increases by 11.8% compared with the benchmark and sum-rate and gradually goes up to 20.7% when \(\sigma^{2}=1\). In addition, the proposed algorithm outperforms the max-rate by a gap from 0-7% with the \(\sigma^{2}\) variation from 0 to 1. It is because LMRSS considers residual energy conditions of each sensor node together with the energy consumption rate when making relay selection, while sum-rate and max-rate only concentrate on energy consumption. As a consequence, the bigger the energy difference degree is, the better lifetime performance the proposed algorithm can get. In fact, the simulation results indicate that LMRSS always outperforms in the comparison in terms of network lifetime under different numbers of sensor nodes in the body-shaped model. For space restriction, the results are not presented here. However, the same trend of performance deviation under different numbers of nodes is illustrated in a more general WBAN model, which can be referred to Figure 8. It should also be noticed that the sum-rate algorithm is always the same with the benchmark in terms of lifetime, which means that this algorithm loses effectiveness in the environment of WBANs. The reason is that, in WSNs, distances between transmitters and receivers are much larger than WBANs. Figure 3: Network lifetime performance comparison.