## 4 Simulation Results
### A Single Congested Link  
We consider four cases where a single congested link is shared by 10 flows, as depicted in Figure 3a. In the first case, the flows are indexed from 1 to 10; hence, the MMFSR is 1.4 Mbps. The simulation results are depicted in Figure 4. In CHOKe and FIFO, the shared bandwidth of flows 1 to 5 is roughly proportional to their MARs. Accordingly, their NBRs are close to constant. Flows 6 to 10 have the same MBR at 10 Mbps, so they fairly share the grabbed bandwidth from flows 1 to 5. Again, their NBRs maintain a constant value. FIFO is the simplest scheme, but it shows the worst fairness. Although CHOKe performs better than the FIFO, it can provide only limited fairness. In AFQ, the NBRs of flows 1 to 5 reach the largest values, and the NBRs of flows 6 to 10 reach the lowest values. In other words, AFQ achieves the best fairness. The NBRs of flows 1 to 5 in AFQ, RPQ and CSFQ all decrease when MAR is close to MMFSR because those flows are more likely to be discarded because of traffic burstiness. From the simulations, AFQ outperforms RPQ, and RPQ outperforms CSFQ in fairness. Therefore, ARQ can effectively protect the fairness of non-aggressive flows from damage due to aggressive flows. Figure 3: Network topologies. (**a**) A single congested link. (**b**) Multiple congested links. In the second case, we consider that all flows are composed of aggressive flows. The MAR of each flow is larger than the MMFSR (1 Mbps). The simulation results are depicted in Figure 5. Compared with the first case, flows 6 to 10 can obtain less additional bandwidth from flows 1 to 5 in CHOKe and FIFO. However, they have larger NBRs because the MMFSR is smaller in this case. CHOKe and FIFO have better fairness for two reasons: flows have approximate MARs, and the MBR of each flow is larger than the MMFSR. Similarly, RPQ and CSFQ both demonstrate better fairness; in addition, they both demonstrate approaching fairness. Repeatedly, AFQ achieves the best fairness. Consequently, RPQ can fairly allocate bandwidth under extreme traffic conditions where all flows are aggressive flows. Figure 4: The Normalized Bandwidth Ratio (NBR) achieved by each of the ten flows sharing a bottleneck link; flows 1 to 5 belong to non-aggressive flows, and flows 6 to 10 belong to aggressive flows. Figure 5: The NBR achieved by each of the ten flows sharing a bottleneck link, with all flows belonging to aggressive flows. In the third case, we consider flows consisting of three magnitudes of MARs, where the MMFSR is 1.375 Mbps. The MARs of flows 1 to 3 and flows 4 to 6 equal 0.5 Mbps and 1 Mbps, respectively. In addition, the MAR of flows 7 to 10 is 6 Mbps. The simulation results are depicted in Figure 6. The MARs of flows 1 to 6 is smaller than the MMFSR, so their NBRs are constant in CHOKe and FIFO. In RPQ and CSFQ, the NBRs of flows 1 to 3 are larger than those of flows 4 to 6. Flows 1 to 3 have lower MARs, so they have less chance of being mistakenly discarded. The MARs of flows 4 to 6 are close to the MMFSR; hence, their arriving packets are more likely to be discarded during traffic burstiness. The NBRs of AFQ are better than those of RPQ and CSFQ. As a result, RPQ still keeps the best fairness under various traffic conditions. Figure 6: The NBR achieved by each of the ten flows sharing a bottleneck link, with flows consisting of three magnitudes of Mean Arrival Rate (MAR)s.  
Figure 7: The NBR achieved by each of the ten flows sharing a bottleneck link, with diverse MARs. In the fourth case, we consider that all flows belong to aggressive flows but that their MARs are diverse. The simulation results are depicted in Figure 7, and the MMFSR is 1 Mbps. Flow 1 is the only non-aggressive flow, which has a lower NBR due to larger traffic burstiness. FIFO still keeps the worst NBRs, whose trends are proportional to the MAR of each flow. We find that traffic load dominates the fairness of FIFO. Additionally, CHOKe is affected due to the same reason, but its fairness is better than that of FIFO.