## 6 Experimental Evaluation
### Experiment II: Service Allocation
#### 6.2.4 Example of How Auction Formulas Work in the Simulation  
The examples below illustrate how bids are defined in our auction algorithms using the same simulation settings as those employed in the evaluation of Ubunye's resource allocation strategy. Example Using the Ubunye Latency Bid Formula  
We calculated the bids of six edge nodes using Equation (1) and determined the winner based on the highest bid. We started with six edge nodes, each with different values for latency (\(L_{ij}\)), available CPUs (\(P_{j}\)), and available memory (\(M_{j}\)). The values for the six edge nodes are as follows in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Edge Node** & \(L_{ij}\) & \(P_{j}\) & \(M_{j}\) \\ \hline
1 & 0.05 & 5 & 11 \\
2 & 0.10 & 9 & 14 \\
3 & 0.03 & 3 & 5 \\
4 & 0.07 & 6 & 10 \\
5 & 0.06 & 7 & 9 \\
6 & 0.09 & 8 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values for latency (\(L_{ij}\)), available CPUs (\(P_{j}\)), and available memory (\(M_{j}\)) for six edge nodes. Bids calculation:  
Node 1:  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]  
\[B_{i1}=|\log_{10}(20)|+|\log_{10}(5)|+|\log_{10}(11)|,\]  
\[B_{i1}=1.301+0.699+1.041=3.041.\]  
Node 2:  
\[B_{i2}=|\log_{10}(1/0.10)|+|\log_{10}(9)|+|\log_{10}(14)|,\]  
\[B_{i2}=|\log_{10}(10)|+|\log_{10}(9)|+|\log_{10}(14)|,\]  
\[B_{i2}=1+0.954+1.146=3.100.\]  
Node 3:  
\[B_{i3}=|\log_{10}(1/0.03)|+|\log_{10}(3)|+|\log_{10}(5)|,\]  
\[B_{i3}=|\log_{10}(33.33)|+|\log_{10}(3)|+|\log_{10}(5)|,\]  
\[B_{i3}=1.522+0.477+0.699=2.698.\]  
Node 4:  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]0  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]1  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]2  
Node 5:  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]3  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]4  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]5  
Node 6:  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]6  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]7  
\[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]8  
The bids for each node are summarized in the following in \[B_{i1}=|\log_{10}(1/0.05)|+|\log_{10}(5)|+|\log_{10}(11)|,\]9  
Conclusion: The winning node is Node 2, with the highest bid of 3.100. Example Using the Ubunye Bandwidth Bid Formula  
We calculated the bids of six edge nodes using Equation (2) and determined the winner based on the highest bid. We started with six edge nodes, each with different values for \begin{table}
\begin{tabular}{c c} \hline \hline
**Edge Node** & \(B_{ij}\) \\ \hline
1 & 3.041 \\
2 & 3.100 \\
3 & 2.698 \\
4 & 2.932 \\
5 & 3.021 \\
6 & 3.063 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Bids for each node—Latency formula. bandwidth (\(BW_{ij}\)), available CPUs (\(P_{j}\)), and available memory (\(M_{j}\)). The values for the six edge nodes are as follows in Table 6.  
Bids calculation:  
\[B_{i1}=|\log_{10}(50)|+|\log_{10}(5)|+|\log_{10}(11)|,\]  
\[B_{i1}=1.699+0.699+1.041=3.439.\]  
Node 2:  
\[B_{i2}=|\log_{10}(40)|+|\log_{10}(3)|+|\log_{10}(12)|,\]  
\[B_{i2}=1.602+0.477+1.079=3.158.\]  
Node 3:  
\[B_{i3}=|\log_{10}(60)|+|\log_{10}(6)|+|\log_{10}(15)|,\]  
\[B_{i3}=1.778+0.778+1.176=3.732.\]  
Node 4:  
\[B_{i4}=|\log_{10}(45)|+|\log_{10}(7)|+|\log_{10}(14)|,\]  
\[B_{i4}=1.653+0.845+1.146=3.644.\]  
Node 5:  
Table 6.0  
Table 6.1  
Node 6:  
Table 6.2  
Table 6.3  
The bids for each node are summarized in the following in Table 6.4  
Bids for each node--Bandwidth formula. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Edge Node** & \(BW_{ij}\) & \(P_{j}\) & \(M_{j}\) \\ \hline
1 & 50 & 5 & 11 \\
2 & 40 & 3 & 12 \\
3 & 60 & 6 & 15 \\
4 & 45 & 7 & 14 \\
5 & 55 & 8 & 9 \\
6 & 35 & 9 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values for bandwidth (\(BW_{ij}\)), available CPUs (\(P_{j}\)), and available memory (\(M_{j}\)) for six edge nodes.