## 5 Evaluation
Before discussing simulation results, the following definitions are necessary: for each flow, _end-to-end flow delay_ will be used to denote the average per-packet end-to-end delay, for all packets forwarded by that flow. End-to-end delay for a packet is the interval between that packet's first transmission attempt at the source of the flow and the time when the packet is successfully received at the destination of the corresponding flow. For the rest of the section, average flow delay will be referred to as flow delay. Figures 6-8 present average flow delay for the three topologies described in Figure 2 and the four SINR threshold values considered. For the rest of the section, end-to-end flow delay will be referred to as _flow delay_. As these figures show, for all three topologies explored, TOFRA-IAN achieves the same delay with BP\({}_{\ell 2e}\), for all \(\gamma\) values considered. The only exception to this is the simulated scenario based on topology 3, with \(\gamma\) = 0.5. In this scenario, TOFRA-IAN also assigns flow on path \(1\to R\to d\). The flow assigned on path \(1\to R\to d\) is also increased in the case where TOFRA is combined with SIC. As Table 3 for example shows, for the second topology and \(\gamma\) = 0.5, TOFRA assigns 0.350 packets per slot on path \(1\to R\to d\), when SIC is applied at both \(R\) and \(d\). Consequently, a larger number of packets will experience queueing delay at \(R\) and also increased retransmissions due to inter-path interference. The effect of queueing delay on flow delay is extensively discussed in the rest of the section. This effect is also validated if BP\({}_{wb}\) is considered for topologies 1 and 2. In these topologies, BP\({}_{wb}\) forwards all packets through path \(1\to R\to d\). Figures 6-8 show that it experiences significantly higher flow delay than all other schemes with the exception of full multipath variants FMP-SIC(\(R\)), FIM-SIC(\(R,d\)). The second reason behind the increased delay of TOFRA, when combined with SIC, is related to the accuracy with which the model presented in Section 3 captures the average throughput of a link and is discussed in the next paragraph. To validate the effect of queueing delay on flow delay, the throughput ratio for a relay, along with average queue length are employed. For the case of relay node \(R\), in Figure 2 for example, throughput ratio is defined as: \(\hat{T}(1,R)/\hat{T}(R,d)\). A value for that ratio larger than one would suggest queueing at the relay, since packets arrive at a rate faster than the rate with which they can be serviced (delivered to \(d\)). This results in an unstable queue at the relay node and consequently in packets experiencing unbounded delay. A value for that ratio that is one, would imply a sub-stable queue at \(R\). In this case, packets may experience an increased queueing delay. Additionally, the average queue length for each node, especially for the relays, is calculated from simulated results. Figure 5: Topology 3: AAT per flow allocation variant. Figures 6-8 also show that, for all topologies and \(\gamma\) values explored, FMP-IAN achieves significantly lower flow delay than TOFRA variants that employ SIC, although FMP is expected to experience more failed packets due to increased inter-path interference. In order to explore this delay gap between FMP and TOFRA variants, topology 2, with \(\gamma=0.5\), is used as an example. Moreover, we focus on FMP-IAN and TOFRA-SIC\((R,d)\) variants. As the simulation results show, FMP-IAN indeed experiences a larger number of failed transmission due to noise, signal attenuation, interference, and fading. For link \((0,1)\), this ratio is \(81.0\%\) for FMP-IAN and \(3.6\%\) for TOFRA-SIC\((R,d)\). As far as path \(1\to R\to d\) is concerned, it is also interesting to note that FMP-IAN manages to deliver to \(R\), only \(8.3\%\) of the packets sent over link \((1,R)\), while the corresponding value for TOFRA-SIC\((R,d)\) is \(68.6\%\).