## 5 Evaluation
Based on how _best_ path is identified, we explore two variants: in the first one, denoted as BP\({}_{c2e}\), best path is considered as the one exhibiting the highest end-to-end success probability, and is identified through: \(\hat{r}_{k}:\underset{r_{k}}{\text{arg max}}\ \ \prod_{(i,j)\in r_{k}}p_{i/i}^{j}\). In the second variant, denoted as BP\({}_{wb}\), best path is defined as the one that has the _widest_ bottleneck link, which can be formulated as identifying path \(\hat{r}_{k}:\underset{k}{\text{arg max}}\ \underset{(i,j)\in r_{k}}{\text{max}}\ \ p_{i/i}^{j}\). In the first two topologies explored, BP\({}_{wb}\) utilizes path \(1\to R\to d\) to the destination, while in the third one, \(2\to d\). BP\({}_{c2e}\) on the other hand, deploys path \(2\to d\), for all three topologies explored. Applying SIC for the cases of the best-path variants and the topologies presented in Figure 2 is meaningless since, when path \(2\to d\) is used, destination \(d\) receives no interference, while in the case of \(1\to R\to d\), the interference received at \(d\), from \(1\), is insignificant due to the large distance between them. For both aforementioned best-path variants, the flow assigned on the utilized single path is calculated by solving a single-path version of the optimization problem (P2), presented in Section 3, through the simulated annealing technique. Different simulation scenarios are generated as follows: for each topology presented in Figure 2, one of the aforementioned flow allocation schemes is employed. For each flow allocation scheme, three variants are simulated based on how interference is handled at each receiving node. The variant denoted by _FMP-IAN_ for example, assigns one packet per slot on each path, while interference is treated as noise at each receiver. For _FMP-SIC(R)_, SIC is assumed at receiving node \(R\). To capture the effect of interference on success probability, four different SINR threshold values are employed: 0.5, 1.0, 1.5, and 2.0. In each simulation scenario, flows carrying constant bit rate, UDP traffic, are generated while the simulation period is \(20,000\) slots. Queues for flow originators are kept backlogged for the whole simulation period. For the relay node present in Figure 2, the queue may become empty during a slot, i.e, queues for relay nodes are not assumed to be saturated in all the simulated scenarios. In the first part of the evaluation process, we explore whether the proposed model accurately captures the average aggregate flow throughput (AAT) observed in the simulation results. Tables 3-5, summarize the flow rates assigned on each path, along with  
Figure 2: A summary of the considered wireless network topologies. the corresponding value for AAT achieved by TOFRA, derived from both the numerical and the simulation results. Recall that flow rates assigned on each path are identified by sources, by solving a topology specific instance of the flow allocation optimization problem presented in Section 3. The path loss exponent assumed for deriving numerical results is 3.0 and link distances are those presented in Figure 2.  
The average deviation between the AAT derived from the model described in Section 3 and the one observed in the simulated results, is 1.42%, over all topologies, \(\gamma\) values, and TOFRA variants employed. There are several reasons for this deviation. The main one is related to the assumption of the model, for AAT, concerning saturated queues at the relay nodes. In our analysis, it is assumed that whenever a relay node attempts to transmit a packet, there is always one available in its queue. In the simulated scenarios, however, a relay node's queue may be empty at a specific slot. In this way, the considered model for the AAT overestimates the interference experienced by any link in the simulated scenarios and thus, underestimates the average throughput achieved over that link.