## 5 Performance Evaluation
Under the same transmission range, load-similar distribution achieves longer network lifetime than uniform node distribution (by up to 32%) for all ranges and non-uniform node distribution (by up to 73%) when \(r<80\) m. This confirms that the load-similar node distribution is more suitable for PMRC-based network than the other two distributions. When \(r\geq 80\) m, there is no significant difference between the network lifetime for load-similar distribution and non-uniform distribution as the network lifetime ends when all source nodes are exhausted. Figure 10 presents the number of network formations _vs._ transmission range \(r\). Generally, the number of network formations shows an increasing trend followed by a decreasing trend with the increase of \(r\). When the transmission range is getting larger, more candidate cluster heads are available, which leads to more rounds of network formations. For \(r\geq 80\) m, the average load at layer 1 is decreased, which leads to the longer average time per round (_i.e._, the average time between two network formations). As a result, the number of network formations drops. Figure 8: Time to first node death _vs._\(r\). Figure 9: Network lifetime _vs._\(r\). Figure 11 shows the average residual energy _vs._ layer ID when \(r=40\) m. Layers with larger layer ID are the ones farther away from the sink. The residual energy at each node is directly related to the load carried by each node. The closer to the sink, the heavier the traffic load and thus higher energy consumed for data communication. The average residual energy of the uniform distribution shows an increasing trend with the increase of layer ID, which is consistent with the load distribution analysis. The residual energy of both the load-similar distribution and nonuniform distribution is better balanced than the uniform distribution in most layers. However, the lifetime of nonuniform distribution is shorter than that of load-similar distribution and eventually more energy is wasted. Figure 12 shows the average packet latency _vs._ transmission range \(r\). In general, the average packet latency deceases with the increase of transmission range \(r\). For the same \(R\), with the increase of \(r\), less layers are generated in the network; then the average number of hops traversed by each packet is decreased, which leads to a lower packet latency. Under the same transmission range, the load-similar distribution significantly reduces packet latency. This is due to the fact that during network lifetime, the number of layers in the load-similar distribution grows much slower than that in the uniform distribution and slower than that in the nonuniform distribution. That is, of the three schemes, the average number of hops traversed in the load-similar distribution is the smallest. The superiority of load-similar distribution is more evident when the transmission range is smaller. Figure 10: Number of network formations _vs._\(r\). Figure 11: Average residue energy _vs._ layer ID (\(r=40\)\(m\)). Figure 13 presents the data delivery ratio of three distribution strategies _vs._ transmission range \(r\). The data delivery ratio of both the load similar distribution and nonuniform distribution is better than that of uniform distribution, especially when the transmission range is smaller. Packets that are not delivered include those lost during network reformations, and those left in the queues when network lifetime ends. The latter part dominates the overall number. As an effect of the load distribution, in uniform distribution, the traffic is more congested at those cluster heads closer to the sink than the other two distributions. The result is that more packets are left in queues in uniform distribution than the other two distributions.