## 6 Numerical Results
### Energy Consumption of Measurements Formation in MLMS Construction and Maintainance
As shown in Figure 10B, at the beginning of increasing the density of interested nodes, control messages of all schemes increase sharply, but the difference is that the MLMS-CC tends to increase slowly after intensity ratio equal to 50% which is less than MLMS (60%) and PB-CDG (70%). This is  
Figure 9: Comparison of MLMS measurement formation and other methods. (**A**) Experiment of the influence of the number of measurements; (**B**) Experiment of the influence of the density of the network. because if the interested nodes have accounted for a certain part of nodes in the network, continuing to increase the number of interested nodes will lead to a high efficiency of constructing groups in MLMS method, therefore the MLMS-CC and MLMS methods are not severely affected. In the performance evaluation of using the Piggyback mechanism to process node failures, we respectively simulated the influence of network size (number of nodes 500 and 1000) and intensity of interested nodes (30% and 60% of nodes in the network). Each node on a MLMS path may fail with a probability of 1%-7% during the measurement-formation periods. The experiment results are shown in Figure 11A, we can see that both the network size and density of the interested nodes will have a greater impact on the Piggyback mechanism, but the impact of network size is significantly larger than that of the intensity of interested nodes (for example, under the condition of node failure rate = 7%, if the number of network size doubles (from 500 to 1000), the number of packets increases 205.46%,  
Figure 10: Comparison of the number of control messages of MLMS measurement formation and other methods. (**A**) Experiment of the overhead of the construction of measurement-formation paths (interested nodes of each measurement account for 50% of nodes in network); (**B**) Experiment of the influence of the number of interested nodes. while if node density doubles (from 30% to 60%), the number of packets only increases 42.17%). This is because when the network size increases, it will inevitably lengthen the MLMS paths, which will result in a remarkable overhead increase in returning failure-node information in the Piggyback mechanism; however, increasing the density of interested nodes does not have a significant influence. Because nodes in the network communicate over an erasure channel, by setting the bit error rate (BER) of this channel, we are able to generate a random packet losses context. We simulated the proposed NACk mechanism and the hand-shaking negotiation mechanism on a 1000-node network (the intensity of interested nodes is 50%). The experimental results are shown in Figure 11B. We can easily find the differences between these two mechanisms. With the increasing of the BER, packets transmission in the NACk mechanism increase more rapidly than in the negotiation mechanism. Specifically, when the BER is relatively small, using NACk mechanism will incur less number of control packets; when BER is around 0.4 \(\times\) 10\({}^{-4}\)-0.5 \(\times\) 10\({}^{-4}\) (in this case, the packets successful delivery rate  
Figure 11: Overhead of maintaining measurement-formation paths. (**A**) Influence of nodes failure; (**B**) Influence of packets loss. is about 95%), both mechanisms have a similar performance, and if we still increase the error rate, the negotiation mechanism will outperform the NAck. This means that, when the network conditions are poor, the negotiation mechanism will be a better choice.