## 5 Evaluation
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Topology**} & \multirow{2}{*}{\(\gamma\)} & **Flow Allocation** & \multirow{2}{*}{\(q_{1}\)} & **\multirow{2}{*}{\(q_{2}\)**} & **AAT\({}_{num}\)** & **AAT\({}_{sim}\)** \\  & & **Scheme** & & 1.0 & 1.005 & 1.004 \\  & & & & 1.0 & 1.084 & 1.116 \\  & & & & 1.0 & 0.945 & 0.942 \\  & & & & 1.0 & 0.889 & 0.886 \\  & & & & 1.0 & 0.975 & 1.023 \\  & & & 1.0 & 0.919 & 0.916 \\  & & & & 1.0 & 0.815 & 0.817 \\  & & & 1.0 & 0.896 & 0.958 \\  & & & 1.0 & 0.894 & 0.894 \\  & & & 1.0 & 0.760 & 0.764 \\  & & & 1.0 & 0.833 & 0.901 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation vs. numerical results for the AAT achieved by each TOFRA variant. Topology 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Topology**} & \multirow{2}{*}{\(\gamma\)} & **Flow Allocation** & \multirow{2}{*}{\(q_{1}\)} & **\multirow{2}{*}{\(q_{2}\)**} & **AAT\({}_{num}\)** & **AAT\({}_{sim}\)** \\  & & **Scheme** & & 1.0 & 1.005 & 1.004 \\  & & & & 1.0 & 1.084 & 1.116 \\  & & & 1.0 & 0.945 & 0.942 \\  & & & 1.0 & 0.889 & 0.886 \\  & & & 1.0 & 0.975 & 1.023 \\  & & & 1.0 & 0.919 & 0.916 \\  & & & 1.0 & 0.815 & 0.817 \\  & & & 1.0 & 0.896 & 0.958 \\  & & & 1.0 & 0.894 & 0.894 \\  & & & 1.0 & 0.760 & 0.764 \\  & & & 1.0 & 0.833 & 0.901 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation vs. numerical results for the AAT achieved by each TOFRA variant. Topology 3.  
should also be noted that the gain in terms of throughput, for SIC, is less significant when it is applied only to receiver \(R\). For \(\gamma\) = 0.5, employing SIC at \(R\), instead of IAN, results in 7.7%, 3.7%, and 3.1% higher AAT, for the three topologies explored. Applying SIC on \(R\), increases the success probability on link \((1,R)\), from 9.3% to 95.1%, for \(\gamma\) = 0.5 and from 2.3% to 81.5% for \(\gamma\) = 2.0. Consequently, transmitter 1 will manage to deliver a larger portion of its traffic to \(R\), when SIC is employed at \(R\), instead of IAN, which will also result in an increased number of packets transmitted from \(R\) to \(d\). This will have a negative effect on the average throughput of link \((2,d)\) since it will experience increased interference. Focusing on the first topology presented in Figure 2, \(\gamma\) = 0.5 and the TOFRA flow allocation scheme we observe the following; when interference is treated as noise at all receivers, the fraction of data packets transmitted over \((2,d)\) that are retransmitted due to noise, signal attenuation, interference, and fading, is 2.7%. In the scenario where SIC is employed at \(R\), the corresponding fraction of retransmitted packets increases to 14.1%. This shows that improving the success probability at a relay node by applying SIC, will also increase the interference imposed on its next hop. Consequently, the number of packets that are retransmitted will increase, limiting the gain in terms of AAT. As Tables 3-5 also show, for higher \(\gamma\) values, applying SIC instead of IAN, for the case of TOFRA, either offers insignificant gain or results in lower average aggregate throughput. As already discussed, applying SIC at \(R\) significantly increases the success probability on link \((1,R)\), with TOFRA also increasing the amount of flow assigned on path \(1\to R\to d\). However, if the increased interference on link \((2,d)\) is not compensated by the gain of utilizing path \(1\to R\to d\), the average aggregate flow throughput (AAT) observed, may be lower compared to the case where IAN is applied at each receiver. As far as the relation between interfering links asymmetry and gain in terms of throughput of SIC over IAN is concerned, the following remark is also interesting. As already discussed above, the success probability of link \((1,R)\) increases from 9.3% to 95.1%, for \(\gamma\) = 0.5, when SIC is employed at \(R\), instead of IAN.