## 6 Experiments and Discussion
### Experiments  
In our experiments, we assume that there are no potential failures negatively affecting the execution of the algorithms (e.g., communication breakdowns, deaths of agents, mis-behavior of agents, etc. ), and the communication is not affected by any noise worsening the quality of the transmitted messages. In addition, all the agents are assumed to be homogenous in the transmission range, communication, computation capabilities, and other aspects affecting the execution of the algorithms. At first, we focus our attention on an analysis of the number of sent messages in Scenario 1 with the best-connected agent selected as the leader. From the results depicted in Figure 10 (blue bars), it can be seen that a decrease in \(P\) results in an increase in the number of sent messages for each analyzed algorithm. Thus, the best performance of all examined algorithms in terms of the number of sent messages is achieved when the value of \(P\) is equal to 0.1. In addition, the highest performance is achieved by \(BG\), which significantly outperforms all the other algorithms for each value of \(P\). Besides, a decrease in \(P\) has only a marginal impact on the performance of \(BG\) in contrast to the other algorithms--the sent messages take the values from this interval [22; 88]. In addition, a decrease in \(P\) ensures that the difference in the performance between \(BG\) and the other algorithms is increased. The second-best performing algorithm is \(PS\) followed by \(PP\), the third-best performing algorithm. However, the difference between these two algorithms in the number of sent messages required for consensus is almost negligible except for lower values of \(P\). The sent messages are from the interval \([180,780]\) in the case of \(PS\) and from \([180,840]\) in the case of \(PP\). Thus, these algorithms require much more messages for consensus than previously discussed \(BG\). The fourth best-performing is \(RG\), the sent messages of which are from the following interval \([193.5,968]\). The worst performance is achieved by \(GG\), whose sent messages take the following values [225; 1085]. Moreover, it is seen that a decrease in \(P\) causes that the difference in the performance between these algorithms and the difference between these two algorithms and the others to increase. As mentioned above, we compare two scenarios determining the way to bound the algorithms in order to identify whether it is better to stop the algorithms according to the current arithmetic mean estimates or the current network size estimates. The results presented in this paragraph and their comparison with those from the previous one help identify the optimal way to bound the algorithms. In the following, we turn our attention to Scenario 2, and the sent messages required for consensus achievement with the best-connected agent selected as the leader are analyzed again. Thus, in this paragraph, we present the results of the same experiments as in the previous one with the difference that the stopping criterion (11) is applied instead of (10). The purpose of this analysis is to identify the optimal way to bound the algorithms. The results for Scenario 2 are shown in Figure 10 (red bars). Again, it is seen that a decrease in \(P\) results in an increase in the number of sent messages regardless of the applied algorithm. As in Scenario 1, thebest performance is achieved by \(BG\) (the number of sent messages is from the interval \([100.5,167.5]\), and the value of \(P\) has only a marginal impact on the performance of \(BG\)), the second-best by \(PS\) (\([780,1320]\)), the third-best by \(PP\) (\([840,1440]\)), the fourth-best by \(RG\) (\([955,1717]\)), and the worst performance is achieved by \(GG\) (\([1078,1923]\)). Again, a decrease in \(P\) causes that the difference in the performance between the algorithms to increase.