## 5 Performance Evaluation
### Simulation and Analysis  
To illustrate the performance of the proposed algorithm, the simulations are performed in Matlab. Each round consists of a clustering phase, multi-hop routing phase and data transmission phase. In the clustering phase, a set of cluster heads is elected and the remaining nodes become cluster members. In multi-hop routing phase, multi-hop route is set up. In the data transmission phase, each cluster member node sends a fixed amount of data to its cluster head, and each cluster head aggregates the received data and then transmits to the base station by multi-hop routing. We firstly consider a wireless sensor network with \(N=200\) nodes randomly uniformly distributed in a 200 m \(\times\) 200 m area. Without loss of generalization, the base station is located at [100, 250]. Assume that collisions, packet losses, and errors are dealt with at the lower layers of the protocol stack. To demonstrate the benefits of REEMR, the performance of this protocol is compared with the other typical protocols, LEACH [7], MOECS [5], CHEF [10] and PEGASIS [14], as indicated in the Section 1. The radio parameters used in our simulations are shown in Table 1. All simulation results are expressed in averages taken over 1,000 random independent experiments. \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Initial energy per node & 2 J \\ \(E_{elec}\) & 50 nJ/bit \\ \(\epsilon_{fs}\) & 10 pJ/(bit\(\cdot m^{2}\)) \\ \(\epsilon_{mp}\) & 0.0013 pJ/(bit\(\cdot m^{4}\)) \\ \(d_{0}\) & 87 m \\ \(E_{DF}\) & 5 nJ/(bit\(\cdot\) signal) \\ Size of a data packet & 500 bits \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 10: Cluster formation of LEACH. The cluster formations of LEACH and REEMR in the same round are shown in Figures 10 and 11. In LEACH, some cluster heads are close each other, and cluster member nodes in each cluster are uneven because LEACH depends only on the probability model to select cluster heads. On the other hand, as REEMR considers the node residual energy and local topology, the cluster heads in REEMR are more even than those in LEACH. The network lifetime is the most important performance metric for WSNs. In [24], the network lifetime is defined as the time until the first node fails or runs out of energy. According to the definition, we can define the network lifetime as the round until the first node runs out of energy. To further evaluate the REEMR's performance with respect to scalability, we employ two different network sizes, namely \(N=200\) and \(N=400\). Figure 12 demonstrates that the network lifetime of REEMR is longer than that of the other protocols, and the scalability of REEMR is better than of the other protocols. In REEMR, the first node death occurs after 4,999 rounds and 6,081 rounds for network size of 200 and 400 nodes, respectively. Under the first node death criterion REEMR extends the network lifetime approximately 13% compared to CHEF, 42% compared to PEGASIS, 77% compared to MOECS, and 156% compared to LEACH. This is because REEMR considers the residual energy, the number of neighbors, and the centrality that influence energy consumption to elect cluster heads. Furthermore, cluster heads construct a reliable multi-hop route which is not easily broken, but also reduces the control overhead. In REEMR, all the sensor nodes can consume the energy evenly, and so the energy consumption of the networks is balanced. As LEACH randomly chooses the cluster heads and their distribution is not uniform, some cluster heads may have too many cluster member nodes. Therefore, these cluster heads may consume much energy and die too soon. MOECS considers multiple parameters such as the distance of a node to the cluster head and residual energy to select cluster heads, which help sensor nodes achieve balanced energy dissipation to prolong the network lifetime. CHEF considers the energy and local distance to choose the optimal cluster heads, which are uniformly deployed in the networks.