## 5 Evaluation
Taking into account these ratios, TOFRA-SIC\((R,d)\) is expected to experience higher queueing delay than FMP-IAN. Indeed, the average queue length for relay node 1 is \(0.09\) packets, for the case of FMP-IAN, and \(17.0\) packets when TOFRA-SIC\((R,d)\) is employed. Comparing different TOFRA variants in terms of average flow delay shows that when SIC is applied, instead of IAN, average flow delay exhibits a significant increase. As Tables 3-5 show, when TOFRA is combined with SIC, maximum AAT is achieved by utilizing path \(1\to R\to d\) in parallel with \(2\to d\), for all topologies explored. The gap in terms of delay may imply that TOFRA variants that employ SIC experience increased queueing delay. To validate this, the simulation scenario based on topology 2 with \(\gamma=0.5\), is used as an example. First, the throughput ratio for relay node \(R\) is estimated, for the two TOFRA variants that employ SIC, from simulation results. The value of this ratio is 1.02, and 1.01, respectively, for the two considered variants, suggesting that the queue at \(R\) becomes unstable. However, as already discussed in the first part of the evaluation process, the model employed for the average aggregate flow throughput, may underestimate the actual average throughput of a link observed in the simulation scenarios. In this way, the average throughput of a specific link may be higher than the average throughput of a subsequent link which results in an _unstable_ queue at the relay. The second reason is that SIC improves the success probability of link \((1,R)\) and, thus, increases the number of packets that are successfully delivered to \(R\), when compared to TOFRA-IAN, resulting in a larger average queue size. For all topologies and \(\gamma\) values explored, when full multipath (FMP) is combined with SIC, either at \(R\), or both at \(R\) and \(d\), it experiences by far higher average flow delay than all other flow allocation schemes discussed. For topology 1, in Figure 2 and \(\gamma=0.5\) for example, the flow delay observed in the simulation results, for FMP-SIC\((R)\) and FMP-SIC\((R,d)\), is 2133.9 and 2111.3 slots, respectively. However, this is expected, since FMP assigns traffic on paths in an interference-unaware manner, experiencing a large number of failed packets due to increased interference. Secondly, it does not adjust the flow assigned on a path based on the one that can be serviced by its bottleneck link, resulting thus, in unstable queues at the relay nodes. For the case of topology 1 with \(\gamma=0.5\) mentioned above, the throughput ratio at \(R\) for FMP-SIC\((R)\) and FMP-SIC\((R,d)\) is 3.680 and 3.658, respectively. As a brief overview of the results concerning flow delay, when TOFRA is combined with SIC, either at the relay or at both the relay and the destination, the delay achieved is significantly worse than TOFRA variant that treats interference as noise (TOFRA-IAN). The reason is that in all simulated scenarios, TOFRA-IAN forwards all traffic to the destination through a single hop path \(2\to d\). Consequently, packets do not experience a queueing delay at relay node \(R\) as in the case of TOFRA-SIC\((R)\) and TOFRA-SIC\((R,d)\). In the final part of the evaluation process, we explore the accuracy with which the simulated annealing method approaches the flow rates that achieve the globally maximum AAT. Towards this direction, a brute force search algorithm is implemented. The brute force algorithm explores all different combinations, of values for the optimization problem's  
Figure 8: Topology 3: flow delay per flow allocation variant. variables. Different values of a specific variable are generated using a specific step size with values for that variable ranging in \([0,1]\). Our goal is to compare the solution to the flow allocation problem identified by the simulated annealing and the brute force algorithm.