# A Mathematical Model for Efficient and Fair Resource Assignment in Multipath Transport
## 5 Performance Evaluation
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Scenario 15**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[i,l] & 15.0 & 15.0 & 10.0 & 15.0 & 10.0 \\
[i,e] & 5.0 & 5.0 & 10.0 & 5.0 & 10.0 \\
[a,c] & 15.0 & 8.3 & 15.0 & 8.3 & 12.5 \\
[a,f] & 10.0 & 8.3 & 10.0 & 8.3 & 12.5 \\
[m,n] & 10.0 & 8.3 & 10.0 & 8.3 & 10.0 \\ \hline \hline \multicolumn{6}{c}{**Scenario 17**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[i,l] & 25.0 & 25.0 & 25.0 & 25.0 & 20.0 \\
[a,f] & 10.0 & 22.5 & 10.0 & 22.5 & 20.0 \\
[m,n] & 25.0 & 12.5 & 25.0 & 12.5 & 20.0 \\ \hline \hline \multicolumn{6}{c}{**Scenario 18**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\
[i,l] & 15.0 & 21.7 & 15.0 & 21.7 & 15.0 \\
[i,e] & 10.0 & 6.7 & 10.0 & 6.7 & 6.3 \\
[a,c] & 12.5 & 8.3 & 12.5 & 8.3 & 11.3 \\
[a,f] & 10.0 & 15.0 & 10.0 & 15.0 & 11.3 \\
[m,n] & 12.5 & 8.3 & 12.5 & 8.3 & 11.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Flow set and LP results for the flows’ end-to-end throughput for scenarios 15 to 18 described in Figure 16. All values in Mbps. Figure 20: Scenario 8—Meshed network. The numbers specify the link speeds in Mbps. The multipath fair capacity allocation models developed in Section 3 are based on fair capacity allocation to individual flows utilizing maximum possible network capacity. It is essential to validate the developed models confirming the optimum solution. If the developed models provide the ideal fair allocation for any scenario, then the models can be confirmed as the optimum fair solution. As an alternative solution which complements the linear programing approach, algorithms which provide an ideal solution for a network scenario for different fair allocation methods have been proposed in [1]. These algorithms resemble the way how one would solve the problem \"manually\" when looking at it. The values of the performance metrics for BSF, BFF and NFF are listed in Tables 10-14. For all investigated scenarios, the performance metrics yield the same value for both the linear programming solution and the algorithmic solution, therefore the results from the algorithmic solution are not given separately. The identity of the LP and the algorithm values confirms the linear programming model as the optimum solution. However, fairness indexes which measure the fairness performance are biased to the equal allocation to the flows and neglect the fairness criteria of the individual allocation methods. Therefore, as already mentioned in Section 4.4, the fairness indexes computed by LP need to be normalized with respect to the respective algorithmic fairness indexes. These normalized values are shown in Figures 21-24. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & \multicolumn{5}{c}{**Scenario 21**} \\ \hline Flow & BSF I & BSF II & BFF I & BFF II & NFF \\  
] & 10.0 & 5.0 & 10.0 & 5.0 & 70.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Flow set and LP results for the flows’ end-to-end throughput for scenarios 21 to 24 described in Figure 18. All values in Mbps.