# A Mathematical Model for Efficient and Fair Resource Assignment in Multipath Transport
## 5 Performance Evaluation
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{4}{c}{**Scenario 25**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[a,d] & 195.0 & 195.0 & 195.0 & 195.0 & 190.0 \\
[e,h] & 15.0 & 15.0 & 15.0 & 15.0 & 10.0 \\
[m,h] & 5.0 & 5.0 & 5.0 & 5.0 & 10.0 \\ \hline \multicolumn{5}{c}{**Scenario 26**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[a,d] & 193.3 & 193.3 & 193.3 & 193.3 & 190.0 \\
[e,h] & 13.3 & 13.3 & 13.3 & 13.3 & 10.0 \\
[m,h] & 3.3 & 3.3 & 3.3 & 3.3 & 5.0 \\
[n,h] & 3.3 & 3.3 & 3.3 & 3.3 & 5.0 \\ \hline \multicolumn{5}{c}{**Scenario 27**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[a,d] & 150.0 & 150.0 & 150.0 & 150.0 & 150.0 \\
[m,d] & 50.0 & 50.0 & 50.0 & 50.0 & 50.0 \\
[e,h] & 20.0 & 20.0 & 20.0 & 20.0 & 20.0 \\ \hline \multicolumn{5}{c}{**Scenario 28**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[a,d] & 100.0 & 100.0 & 100.0 & 100.0 & 100.0 \\
[m,d] & 50.0 & 50.0 & 50.0 & 50.0 & 50.0 \\
[n,b] & 50.0 & 50.0 & 50.0 & 50.0 & 50.0 \\
[e,h] & 15.0 & 15.0 & 10.0 & 15.0 & 10.0 \\
[g,h] & 5.0 & 5.0 & 10.0 & 5.0 & 10.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Flow set and LP results for the flows’ end-to-end throughput for scenarios 25 to 28 described in Figure 19. All values in Mbps. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{4}{c}{**Scenario 29**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[n,h] & 25.0 & 25.0 & 25.0 & 25.0 & 50.0 \\
[m,h] & 25.0 & 50.0 & 25.0 & 50.0 & 50.0 \\
[a,h] & 100.0 & 75.0 & 100.0 & 75.0 & 50.0 \\ \hline \multicolumn{5}{c}{**Scenario 30**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[n,h] & 25.0 & 25.0 & 50.0 & 75.0 & 50.0 \\
[m,h] & 25.0 & 41.7 & 50.0 & 25.0 & 50.0 \\
[a,h] & 75.0 & 66.7 & 50.0 & 25.0 & 50.0 \\
[a,d] & 75.0 & 66.7 & 50.0 & 75.0 & 50.0 \\ \hline \multicolumn{5}{c}{**Scenario 31**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[n,h] & 50.0 & 16.7 & 25.0 & 16.7 & 33.3 \\
[m,h] & 16.7 & 20.0 & 25.0 & 41.7 & 33.3 \\
[a,h] & 16.7 & 70.0 & 50.0 & 66.7 & 33.3 \\
[a,d] & 16.7 & 66.7 & 50.0 & 41.7 & 33.3 \\
[m,e] & 50.0 & 10.0 & 25.0 & 16.7 & 33.3 \\
[n,d] & 50.0 & 16.7 & 25.0 & 16.7 & 33.3 \\ \hline \end{tabular}
\end{table} 
Table 9: Flow set and LP results for the flows’ end-to-end throughput for scenarios 29 to 31 described in Figure 20. All values in Mbps. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & \(Alloc\) & \(\gamma_{\text{Jain}}\) & \(\gamma_{\text{Vard}}\) & \(Alloc\cdot\gamma_{\text{Jain}}\) \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 11: Performance evaluation for BSF-II. \(Alloc\) values in Mbps. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & \(Alloc\) & \(\gamma_{\text{Jain}}\) & \(\gamma_{\text{Vard}}\) & \(Alloc\cdot\gamma_{\text{Jain}}\) \\ \hline
1 & 35.0 & 0.845 & 0.571 & 29.6 \\
2 & 35.0 & 0.860 & 0.714 & 30.1 \\
4 & 35.0 & 0.896 & 0.825 & 31.4 \\
5 & 15 & 1.000 & 1.000 & 15.0 \\
6 & 10 & 1 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & \(Alloc\) & \(\gamma_{\text{Jain}}\) & \(\gamma_{\text{Vard}}\) & \(Alloc\cdot\gamma_{\text{Jain}}\) \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 11: \(Cont.\) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & \(Alloc\) & \(\gamma_{\text{Jain}}\) & \(\gamma_{\text{Vard}}\) & \(Alloc\cdot\gamma_{\text{Jain}}\) \\ \hline
21 & 300 & 0.617 & 0.450 & 185.1 \\
22 & 270 & 0.404 & 0.321 & 109.1 \\
23 & 270 & 0.285 & 0.296 & 77.0 \\
24 & 270 & 0.538 & 0.489 & 145.3 \\
25 & 215 & 0.403 & 0.140 & 86.6 \\
26 & 213 & 0.303 & 0.125 & 64.6 \\
27 & 220 & 0.635 & 0.477 & 139.7 \\
28 & 220 & 0.635 & 0.614 & 139.7 \\
29 & 150 & 0.667 & 0.500 & 100.1 \\
30 & 200 & 0.889 & 0.778 & 177.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Performance evaluation for BFF-I. \(Alloc\) values in Mbps. Figures 21 depicts the aggregate capacity allocation of all flows in the network. All fairness methods achieve the same network utilization for the different scenarios.