## 3 Concept and Working Principle of Competing Miners in a Blockchain
### The Concept of Competing Miners  
Figure 3 shows the concept of a blockchain with competing miners on each participant. (In the EC-enabled blockchain, the participant refers to the edge server. In blockchain EC, it refers to a UAV.) A blockchain with competing miners works as follows:  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Cryptocurrency** & **Transactions per Second** & **Average Transaction Confirmation Time** \\ \hline Bitcoin & 3–7 & 25 min \\ Ethereum & 15–20 & 2 min \\ Ripple & 1500 & 4 s \\ Bitcoin Cash & 61 & 60 min \\ Cardano & 5–7 & 3–5 min \\ Litecoin & 26 & 30 min \\ Monero & 4 & 30 min \\ Neo & 1000 & 15–20 s \\ Dash & 48 & 2–10 min \\ \hline \hline \end{tabular}
\end{table}
Table 1: Transaction speed of different cryptocurrencies.  
Figure 2: PoW hash.  
First, the data created by a participant are sent to multiple competing miners (not a particular single miner, as in the traditional blockchain) to solve the PoW and create a block (step (1) in Figure 3).
* Second, the data are mined by a set amount of competing miners per participant, where they compete on being the first to mine the data into a block (step (2) in Figure 3; in this case, K = 2 miners).
* Third, after mining is finished, the block is sent back to the participant for identification (step (3) in Figure 3). Specifically, if two or more miners complete the mining task almost at the same time, then the participant has to identify which miner completed it first.
* Finally, the participant then broadcasts the mined block to the other participants in the network by performing a cross verification (step (4) in Figure 3), and the cross-verified block is then added to the blockchain (step (5) in Figure 3).  
A blockchain with multiple competing miners requires much less time for solving the PoW compared to a traditional blockchain that employs only a single miner. This significant benefit in turn enables a lower latency and less energy consumption for many EC applications, such as IoT [28; 29], autonomous vehicles and UAVs [11], and healthcare [30]. The details will be investigated in the following sections. The intuitive reason for this benefit is as follows: In the blockchain, the miner solves the PoW by randomly guessing the hash value, which means that the time spent for completing the mining task is random. Thus, if we employ more miners in the blockchain, then the chance of solving the PoW more quickly increases. Mathematically, this result can be shown as follows: Let \(t_{i}\) denote the time spent by miner \(i\) for completing the mining task. If there are a total of \(K\) miners, the completion time is (approximately) given by \(t=\min\{t_{1},t_{2},\cdots,t_{K}\}\), which is a random sequence that is monotonically decreasing in the number \(K\) of miners. Thus, \(t\) decreases as \(K\) increases.  
The idea behind lower energy consumption is that with more miners, the time spent on mining reduces. Therefore, less computing resources are used, which results in less energy consumed. However, the computing capabilities of a device come to a limit. In other words, employing too many miners, more than the device can handle, in the end, requires too many computing resources, which can result in more energy being used.  
Figure 3: The concept of blockchain with competing miners.