## 5 Results and Discussion  
A detailed analysis of the performance of the proposed buffer-aided multi-hop relay (BAMR) selection is presented in this section. This analysis is based on the results obtained using Monte Carlo simulations and includes comparison with contemporary schemes as well. At first, we have conducted simulations with a simple topology consisting of a cluster of two relays with a buffer size of two each, transmission rates of 2 bps/Hz, and the SINR varying from 0 dB to 40 dB. Later, we considered additional topologies with varying combinations of these parameters to validate the results of the first set of simulations. We adopted a distributed approach for the coordination of the relay-pair selection process, in which synchronized timers were used. The process started with the broadcast of a pilot sequence by the source, which was used to estimate the \((S\to R)\) CSI by all K-relays. This was followed by the transmission of the pilot signal by the destination to the relays, which extracted the \((R\to D)\) CSI. After this, each relay took turns in transmitting pilots to the other \(K-1\) relays that calculated the \((R\to R)\) CSI. Concurrently, the LI CSI was estimated. Each relay notified the rest of the \((K-1)\) relays about the status of its buffer. Now, each relay set its timer to be inversely proportional to the level of power required for successful transmission. The outage probability decreased as the number of relays and buffer size increased, and this was evident from the fact that in general, higher diversity is obtained with more relays and a lower drop rate with larger buffer size. This coincides with our results as shown in the next two figures. Figure 12 shows the achieved average end-to-end data rate for BAMR as a function of the number of relays for various values of buffer sizes. The achievable data rate increased as the number of relays increased (higher diversity), primarily due to the availability of more link pairs. Further, for a small buffer size, the performance can degrade, but with relatively larger buffer sizes, the performance significantly improved (reduction in drop rate). In Figure 13, the outage probability as a function of the number of relays for BAMR and three other contemporary schemes is shown. It is to be noted that with the higher number of relays to choose from, the possibility of all relays in outage was reduced. This was evident from that fact that the outage probability decreased as the number of relays increased for all four schemes; however, BAMR achieved the best performance compared to the rest of the three schemes. Figures 14-17 depict the impact of varying the values of SNR on various performance measures such as the data rate, outage, throughput, and delay for BAMR and other contemporary schemes. Figure 14 shows the average end-to-end rate as a function of SNR for BAMR, as well as for the VFD, max-link, and max-max schemes. The BAMR scheme clearly outperformed the other schemes, and the performance gap became significant with the increasing values of SNR. This gain in performance was due to the fact that the proposed BAMR scheme removed the half-duplex limitation, which significantly enhanced the achievable data rate. In Figure 15, the outage probability is plotted as a function of SNR for BAMR and also for the max-link, max-max, and Buffer-Aided Full-Duplex (BAFD) schemes. The results indicated the  
Figure 14: Average data rate vs. SNR. Figure 12: End-to-end rate vs. the number of relays. Figure 13: Outage probability vs. the number of relays. superior performance achieved with BAMR as compared to the performance achieved using the other three schemes. The throughput performance as a function of SNR for the BAMR, as well as for BAFD, max-link and max-max schemes is depicted in Figure 16. BAMR attained the best performance of all the schemes over the range of increasing SNR values, enabling achieving higher data rates, as is shown in Figure 14 as well.