## 4 Proposed Frameworks with the Utilization of Competing Miners
### Blockchained EC with Hierarchical Competing Miners
According to the results shown in Figures 9 and 10, blockchain EC performs much better than the baseline in terms of latency and energy consumption. As expected, the case of four miners yields the best performance at the high difficulty level (i.e., D = 6). Interestingly, however, we observe that at the low difficulty level (i.e., D = 4), the case of three miners yields the best performance (rather than the case of four miners). Finally, in Table 3, by comparing the performance of the baseline and blockchain EC with K = 3 when D = 4, we find that the latter is 157% (i.e., 2.5 times) faster than the former in terms of latency. When D = 5, we can observe that K = 4 is, incredibly, 231% (i.e., 3.3 times) faster than the baseline, which is a significant improvement. In our last experiment, when D = 6, we find that blockchain EC with K = 4 still outperforms the others, with an amazing 254% (i.e., 3.5 times) faster mining speed. When compared to the watt usage, the biggest difference is observed with K = 3 miners, as shown in Table 4. When K = 3 miners are used, the energy consumption is 24% less than the baseline, while using K = 4 miners interestingly proves to consume more energy than the baseline. When D = 5 and D = 6, the case of K = 4 outperforms the others, with 60% and 56% less energy usage, respectively, than that of the baseline of only a single miner, which validates the effectiveness and superiority of our proposed framework. Figure 10: Average energy consumption versus difficulty level D for different numbers (K) of hierarchical competing miners. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Avg Latency** & **D = 4** & **D = 5** & **D = 6** \\ \hline Baseline & 0.36 & 0.73 & 1.17 \\ (single miner) & 0.21 (71\%) & 0.37 (97\%) & 0.65 (80\%) \\ Blockchained EC & 0.14 (157\%) & 0.25 (192\%) & 0.53 (120\%) \\ Blockchained EC & 0.20 (80\%) & 0.22 (231\%) & 0.33 (254\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average latency by K = 1, 2, 3, 4 with faster than the baseline presented in percentage. This framework has some problems with scalability, as the edge devices do not have the same opportunities as the edge servers in adding more competing miners to further improve the results. However, seeing as the results show such good numbers, employing a maximum of four miners would be sufficient for applications using this framework. In addition, to confirm the analysis made in Section 2, we observe that for every miner added, the increased energy consumed does not exceed 35%. Therefore, with the multiple competing miners being able to solve the PoW at faster rates (i.e., more than 35% faster), there is lower energy consumption overall. Furthermore, adding the blockchain before the offloading phase makes a significant improvement when it comes to security. Even if the devices that gather data are being put out in the public, the offloading process will not suffer from security threats. In a standard EC network, the offloading phase has no extra security added to it, but with the blockchain, the data are encrypted and validated before leaving the device, which results in higher security and confirms the significance of our proposed framework.