# An Energy-Efficient Two-Stage Cooperative Routing Scheme in Wireless Multi-Hop Networks
## 4 Simulation Results  
In this section, the simulations are designed to show the effectiveness of the proposed scheme by comparing its performance with the above-mentioned existing schemes via MATLAB. We simulate a network with \(N\) nodes randomly distributed in an \(M\times M\text{m}^{2}\) square area. Part of simulation parameters are shown in Table 1 which is similar to the settings in [10; 20; 29; 32]. Unless otherwise specified, all the outputs are based on averaging over 50 randomly generated topologies each with 100 trials. Each trial starts with all nodes initialized with energy \(E_{\text{ini}}\) and ends while any one node has depleted its energy. For each trial, communication sessions are continually generated each with random chosen source and destination nodes, and each source has one data packet to be transmitted to the destination. The maximum normalized transmission power is \(P_{\text{max}}=400\) units and the initial energy of each node is \(E_{\text{ini}}=2000\) units. For the reason of simplicity, we assume that 1 unit transmit power will consume 1 unit energy during one time slot. The end-to-end delay is measured with the total time slots consumed during the communication session. The complex channel gain \(h_{i,j}\) (\(\forall i\
eq j\)) is zero-mean complex Gaussian with variance being proportional to \(d_{i,j}^{-\alpha}\) where \(\alpha\) is the path loss exponent, and \(d_{i,j}\) denotes the distance between node \(i\) and \(j\). In the following simulations, the MTE, PC-3, FA, and FACR schemes are adopted as the baselines for performance comparison. The evaluated performance metrics include the residual energy of the whole network, network lifetime, average end-to-end transmission delay and energy efficiency. We define the dead node as a node whose energy is depleted. The network lifetime is defined as the time when the first dead node appears, and it can be measured with the number of sessions. The average end-to-end transmission delay indicates the average number of time slots consumed when a packet is transmitted from the source to destination. The energy efficiency is the number of packets arriving at destinations divided by the total energy cost during the network lifetime. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(M\) & 100 & \(E_{\text{ini}}\) & 2000 \\ \(P_{\text{max}}\) & 400 & \(\alpha\) & 2 \\ \(\gamma_{\text{min}}\) & 1 & \(\sigma^{2}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for simulation. In the simulations, the parameter \(x\) in Equations (15) and (16) can be 0, 1, or 2 and the results are labeled as TSCR-0, TSCR-1 and TSCR-2, respectively. The first simulation is to compare the residual energy and lifetime of a fixed network. The results shown in Figure 3 are based on the same fixed network with \(N=100\) nodes and one trial. We can see that TSCR-0 has the best residual energy while TSCR-2 has the longest network lifetime. This is because when \(x=0\), the proposed scheme aims at minimizing the end-to-end energy cost. With a larger \(x\), the residual energy of nodes will have larger influence on the link cost, hence the residual energy of nodes can be more balanced and the network lifetime becomes longer. Obviously, minimizing the end-to-end energy cost is not equivalent to maximizing the network lifetime. As mentioned above, the traditional MTE and PC-3 schemes are designed for an excellent end-to-end performance, like the end-to-end energy cost and the end-to-end transmission delay. It can be seen from the comparison between the network residual energy of TSCR-0 scheme and MTE, PC-3 schemes that the proposed cooperative scheme can save more energy. Meanwhile, FA and FACR schemes are designed for prolonging the network lifetime. Compared with FA and FACR schemes, the proposed TSCR-1 and TSCR-2 schemes have achieved a longer network lifetime which reflects a better energy balance in the network.