## 5 Computational Experiments
### Comparison with Existing Distributed Algorithms
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance Type**} & \multicolumn{3}{c}{**CNP**} & \multicolumn{3}{c}{**DETS**} & \multicolumn{3}{c}{**ADMM**} & \multicolumn{3}{c}{**PITO**} \\ \cline{2-13}  & \(aRV\) & \(aCT\) & \(aRT\) & \(aRV\) & \(aCT\) & \(aRT\) & \(aRV\) & \(aCT\) & \(aRT\) & \(aRV\) & \(aCT\) & \(aRT\) \\ \hline \([\)A, 3, low, emergency\(]\) & 0.0380 & 12 & **0.0172** & 0.0141 & 17.59 & 0.0172 & 0.0103 & 52 & 0.7014 & **0.0014** & **8** & 0.0177 \\ \([\)A, 3, low, normal\(]\) & 0.0427 & 12 & 0.0172 & 0 & 17.85 & 0.0187 & 0.0079 & 52 & 0.6914 & 0.0016 & **8** & **0.0169** \\ \([\)A, 3, high, emergency\(]\) & 0.0450 & 12 & **0.0021** & 0.0196 & 16.00 & 0.0029 & 0.0155 & 52 & 0.3789 & **0.0033** & **7.75** & 0.0031 \\ \([\)A, 3, high, normal\(]\) & 0.0497 & 12 & 0.0228 & 0.0207 & 21.44 & **0.0185** & 0.0105 & 54 & 0.5845 & **0.0028** & **9.36** & 0.0187 \\ \([\)A, 5, low, emergency\(]\) & 0.0449 & 20 & **0.0226** & 0.0274 & 36.00 & 0.0435 & 0.0110 & 50 & 2.5463 & **0.0002** & **15** & 0.0567 \\ \([\)A, 5, low, normal\(]\) & 0.0413 & 20 & **0.0224** & 0 & 36.00 & 0.0431 & 0.0155 & 50 & 2.5087 & 0.0002 & **15** & 0.0591 \\ \([\)A, 5, high, emergency\(]\) & 0.0346 & 20 & **0.0186** & 0.0954 & 38.77 & 0.0438 & 0.0248 & 52 & 2.5411 & **0.0001** & **16** & 0.0565 \\ \([\)A, 5, high, normal\(]\) & 0.0337 & 20 & **0.0192** & 0.0932 & 38.42 & 0.0434 & 0.0280 & 52 & 2.5181 & **0.0006** & **16** & 0.0590 \\ \([\)B, 3, low, emergency\(]\) & 0.0401 & 15 & **0.0030** & 0.0287 & 18.59 & 0.0038 & 0.0239 & 84 & 1.1158 & **0.0022** & **8** & 0.0074 \\ \([\)B, 3, low, normal\(]\) & 0.0383 & 15 & **0.0029** & 0.0250 & 18.65 & 0.0037 & 0.0232 & 84 & 1.1061 & **0.0019** & **8** & 0.0045 \\ \([\)B, 3, high, emergency\(]\) & 0.0436 & 15 & **0.0023** & 0.0459 & 18.74 & 0.0032 & 0.0244 & 87 & 1.0348 & **0.0038** & **9** & 0.0041 \\ \([\)B, 3, high, normal\(]\) & 0.0421 & 15 & **0.0036** & 0.0372 & 23.39 & 0.0048 & 0.0194 & 81 & 1.0032 & **0.0035** & **7** & 0.0046 \\ \([\)B, 5, low, emergency\(]\) & 0.0430 & 25 & **0.0097** & 0.0060 & 36.59 & 0.0309 & 0.0175 & 93 & 6.8399 & **0.0011** & **12** & 0.0409 \\ \([\)B, 5, low, normal\(]\) & 0.0433 & 25 & **0.0180** & 0.0040 & 36.76 & 0.0302 & 0.0158 & 93 & 6.9443 & **0.0010** & **12** & 0.0412 \\ \([\)B, 5, high, emergency\(]\) & 0.0698 & 25 & **0.0191** & 0.0656 & 38.74 & 0.0345 & 0.0481 & 93 & 7.0396 & **0.0004** & **13** & 0.0350 \\ \([\)B, 5, high, normal\(]\) & 0.0691 & 25 & **0.0237** & 0.0552 & 38.34 & 0.1103 & 0.0428 & 93 & 6.0205 & **0.0010** & **13** & 0.0269 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison results for small-scale instances. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance Type**} & \multicolumn{3}{c}{**CNP**} & \multicolumn{3}{c}{**DETS**} & \multicolumn{3}{c}{**ADMM**} & \multicolumn{3}{c}{**PITO**} \\ \cline{2-13}  & \(aRV\) & \(aCT\) & \(aRT\) & \(aRV\) & \(aCT\) & \(aRT\) & \(aRV\) & \(aCT\) & \(aRT\) & \(aRV\) & \(aCT\) & \(aRT\) \\ \hline \([\)C, 10, low, emergency\(]\) & 0.0725 & 50 & **0.0516** & 0.0752 & 76.80 & 0.1100 & 0.0270 & 490.24 & 79.1380 & **0.0004** & **47** & 0.3098 \\ \([\)C, 10, low, normal\(]\) & 0.0778 & 50 & **0.0351** & 0.0661 & 76.35 & 0.1249 & 0.0267 & 490.72 & 78.9001 & **0.0005** & **47** & 0.3202 \\ \([\)C, 10, high, \(]\) & 0.0486 & 50 & **0.0185** & 0.0326 & 65.00 & 0.0729 & 0.0559 & 506.08 & 82.4659 & **0.0009** & **43.28** & 0.3141 \\ \([\)C, 10, high, normal\(]\) & 0.0481 & 50 & **0.0180** & 0.0293 & 65.00 & 0.0713 & 0.0455 & 506.64 & 81.9928 & **0.0008** & **43.78** & 0.3106 \\ \([\)C, 20, low, \(]\) & 0.0961 & 100 & **0.1143** & 0.0703 & 193.82 & 0.5209 & 0.0471 & 1317.76 & 994.6563 & **0** & **92** & 1.0020 \\ \([\)C, 20, low, normal\(]\) & 0.0964 & 100 & **0.1112** & 0.0739 & 193.97 & 0.6528 & 0.0477 & 1317.92 & 993.64 Figure 6a illustrates the fact that PITO achieves minimal \(aRV\) values compared to the three competitors, highlighting its superiority in offloading assignment quality.