## 5 Performance Evaluation  
To evaluate the performance of the proposed load-similar node distribution strategy for the MOL-enabled PMRC-based WSN, extensive simulations have been conducted on the WSN simulation module developed on OPNET modeler. In all simulations, we assume a 250 m \(\times\) 250 m geographical area covered by a sensor network with the sink node located at the center. Table 1 lists the key parameters used in the simulations. Figure 7: A case of node distribution (N = 400, R = 125 m, r = 40 m, sink is located at the area center). **(a)** Load-similar node distribution. **(b)** Uniform node distribution. The following performance metrics are collected:  
_Time to first node death_: in the simulation, we consider only the node death due to drained energy. Generally, this metric reflects the worst lifetime. _Network lifetime_: it is defined as the time when the network is no longer connected or all source nodes drain out their energy. _Number of network formations_: it is defined as the total number of network formations during network lifetime. _Average residual energy_: it is defined as the average residual energy of all sensor nodes at their initial layer when the network lifetime ends. _Average packet latency_: the latency of a packet is defined as the time difference between the time when the packet is generated at the source node and the time when the packet is received at the sink node. _Data delivery ratio_: it is defined as the ratio of the number of data packets received by the sink to the total number of data packets generated in the network. In the following, we present the simulation results of the aforementioned performance metrics for three different node distribution strategies: (1) _load-similar node distribution_, where sensor nodes are deployed following the load distribution analysis in Section 4; (2) _nonuniform node distribution_, where the number of nodes distributed in adjacent coronas \(C_{i}\) (inner) and \(C_{i+1}\) (outer) is initially regulated as \(N_{i}/N_{i+1}=q\) with a common ratio of \(q=2\); and (3) _uniform node distribution_, where sensor nodes are uniformly distributed in the area. The location of each node in these three distributions is generated using Matlab. In each simulation, a portion of sensor nodes (20% in our simulations) are selected as source nodes to generate and send data. Without loss of generality, these source nodes are randomly distributed in the network area. The results shown are the averaged results of 5 sets of source nodes. Figure 8 shows the time to first node death _vs._ transmission range \(r\). In general, the time to first node death for all distributions shows an increasing trend with the increase of \(r\). The first node death typically happens at the first layer. With the increase of \(r\), the average load carried by nodes at layer 1 decreases because they will consume less energy in receiving packets as there are less nodes distributed outside layer 1. Under the same transmission range, the trend for all distributions is not consistent. That is attributed to the fact that the initial network topology also has a significant impact on the time to first node death. However, load-similar node distribution strategy achieves longer time to first node death for most cases. \begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Value** \\ \hline Number of nodes & 400 \\ Radio transmission range & \{40, 60, 80, 100\} m \\ Initial energy per node & 0.5 J \\ Packet generation rate & 1 _pkt/s_ \\ Packet length & 200 Bytes \\ Simulation time & Until network partition \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 9 shows the network lifetime for all distributions increases monotonously with the increase of transmission range \(r\). With the increase of \(r\), the number of candidate cluster heads for each layer increases, which helps prolonging the network lifetime.