# Bloom Filter Approach for Autonomous Data Acquisition in the Edge-Based MCS Scenario +
## 4 Results and Discussion
### Evaluation of BF Algorithm
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Values** \\ \hline _allResults_ & 4,709,259 \\ \hline _announcements_ & 579,040 \\ \hline \(m_{worker}\) & 1; 2; 3; 5 \\ \hline \(m_{MEC}\) & 1; 2; 3; 5; 10; 15 \\ \hline \(window\) (in minutes) & 1; 5; 10; 15; 30; 60; 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Default parameter values. more workers are required per _small_ area by ME host, worker self-deactivation by updating their BF has less influence because there is a need to satisfy application requirements (i.e., ME hosts need to collect \(m_{MEC}\) results before updating their filters). In addition, the results show that savings are generally lower when the BF validity period is shorter due to the increased number of transmitted data readings between workers and ME hosts. Although one might expect that energy savings will follow trends in the number of results submitted by workers (i.e., when the number of useful data increases, the total savings drops), we can see a slight deviation when \(m_{MEC}\) is one due to the overhead introduced by filter update and reset messages. Whenever a worker submits a redundant result to the corresponding ME host, it receives a _global_ filter for the \(km\) MGRS area where it is currently residing (i.e., an updated BF which contains all results received by the ME host in the area), and when ME hosts require just one result per _small_ area, this can occur quite often. That is especially visible for short filter validity periods (e.g., 1 min) when the number of reset messages also increases. Overall, we can see that the total savings are above 53% even in the worst-case scenario when the filter validity period is just 1 min, while it can go up to 62% if filter reset occurs every 120 min. Figure 8: Percentage of data sent by all workers when \(m_{worker}=1\). Figure 9: Energy savings when \(m_{worker}=1\). Figure 10 shows how BF validity period and MCS application requirements influence the total energy savings when the required number of results, which a worker has to produce per _small_ MGRS area before updating its BF (i.e., \(m_{worker}\)), is fixed to one of the default values from Table 1. The results confirm that savings drop when ME hosts require more data readings per _small_ MGRS area and the time between consecutive filter resets is shorter. In particular, the results indicate that a filter validity period of just 1 min significantly reduces the total saving compared to longer filter validity periods (e.g., 5 min) due to the overhead caused by many reset messages. Furthermore, when we compare the total savings in Figure 10a,d, we can see that savings significantly drop with higher values of \(m_{worker}\). If workers are instructed to transmit more results to the edge host, then filtering mechanisms have less influence to reduce the total savings. However, even in the worst-case scenario shown in Figure 10d, when we need high redundancy per _small_ MGRS area (i.e., up to 5 results for every 100 m\({}^{2}\)), the energy savings is around 35% when the time between consecutive filter resets is just 1 min, and can grow up to 55% when filter validity period is 120 min. Next, we analyze how the number of results a worker needs to submit per _small_ MGRS area and the length of BF validity period influence the total savings while keeping the fixed value of \(m_{MEC}\), as shown in Figure 11. The results indicate that when increasing the time between consecutive filter resets (i.e., \(window\)), the influence of the parameter \(m_{worker}\) drops. In other words, when the filter validity period is just 1 min, the difference in savings for \(m_{worker}=1\) and \(m_{worker}=5\) is around 18% (i.e., the total savings is 18% lower when workers are instructed to submit five results per _small_ area), while this difference drops to only 7.5% when filter reset is every 120 min when the parameter \(m_{MEC}\) has a fixed value of 5.