# An Energy-Efficient Two-Stage Cooperative Routing Scheme in Wireless Multi-Hop Networks
## 4 Simulation Results
To further show the effectiveness of proposed TSCR scheme, the network lifetime, average end-to-end transmission delay and energy efficiency are evaluated under different number of nodes \(N\). For each point of \(N\) in Figure 4, the performance is averaged over 50 different network topologies each with 100 trials. It can be seen from the figure that the network lifetime increases with the increase of \(N\) due to increased total energy in the whole network. Meanwhile, more energy can be saved by cooperative routing because a denser network offers more opportunities for cooperative transmissions. The comparison among TSCR-0, TSCR-1 and TSCR-2 shows that the bigger the \(x\) is, the longer the network lifetime becomes, which indicates that the increase of \(x\) can improve the energy balance and prolong the network lifetime. We also observe that when \(x\) changes from 0 to 1, the network lifetime achieves a big improvement while the change from 1 to 2 brings relatively less gains. Furthermore, on the one hand, both TSCR-1 and TSCR-2 outperform the existing schemes in terms of network lifetime, which proves that proposed TSCR scheme improves the energy balance of network. On the other hand, the higher curve of TSCR-0 over MTE and PC-3 indicates that the proposed TSCR scheme is also effective in saving the energy cost in the end-to-end transmission. Figure 3: Residual energy of the whole network versus time with different schemes. The average end-to-end transmission delay indicates the end-to-end performance of transmission schemes. The schemes (MTE, PC-3) to minimize the energy cost generally have lower end-to-end transmission delay than the schemes (FA, FACR) aiming at maximizing the network lifetime. Figure 5 shows the average end-to-end transmission delay versus the different number of nodes. It can be seen from the figure that the end-to-end delay increases with the increase of \(N\). This is because that lager distance leads to larger signal attenuation, a transmission over multiple short hops requires less power compared with a single transmission over a long distance. Therefore, a denser network will offer more opportunities for energy savings and result in a longer end-to-end transmission delay. Meanwhile, TSCR-0 outperforms all the existing schemes which proves the effectiveness of the proposed TSCR scheme in terms of end-to-end performance. Moreover, the end-to-end transmission delay of TSCR scheme increases as \(x\) increases, and the end-to-end performance of TSCR-1 and TSCR-2 is lower than PC-3 scheme because the residual energy is considered in the previous two schemes, which leads to a longer network lifetime. Figure 6 shows the energy efficiency of the proposed TSCR scheme compared with the existing schemes. As shown in the figure, the energy efficiency increases with the increase of \(N\), this is because the increased nodes can prolong the network lifetime, meanwhile, the increased end-to-end transmission delay indicates the less energy cost per end-to-end transmission. It can be also seen from the figure that the proposed TSCR-0 and TSCR-1 significantly outperform the other schemes in  
Figure 4: Network lifetime versus different number of nodes. Figure 5: Average end-to-end delay versus different number of nodes. terms of energy efficiency. Moreover, the energy efficiency of proposed TSCR-2 is higher than FA and MTE schemes. The above results prove that the proposed TSCR scheme can save the energy cost of end-to-end transmission and improve the energy balance of network. In summary, the simulation results indicate that:  
1. TSCR-0 has achieved the lowest end-to-end transmission delay and highest energy efficiency. In contrast, TSCR-2 has achieved the longest network lifetime; Meanwhile, the network lifetime of TSCR-0 is better than that of MTE and PC-3, and the end-to-end transmission performance of TSCR-1 and TSCR-2 is better than that of FA and FACR, which shows that TSCR scheme can improve the end-to-end performance and network lifetime simultaneously. 2.