# Transmission Delay-Based Uplink Multi-User Scheduling in IEEE 802.11 ax Networks +
## 6 Performance Evaluation
### Uplink Transmission in Stable Channel Environment  
Figures 4 and 5 show the network throughput and fairness performance when there are 200 stations in the network. The uplink channels were assumed to be stable; thus, MCSs did not change during the simulation time. As shown in Figure 4, network throughput performance increased as the number of simultaneous uplink transmission increased. For all the uplink cases with a different number of simultaneous transmissions, the proposed delay-based clustering with proportional fair selection performed better than other methods. Note that as \(\alpha\) increases and \(\beta\) decreases, clusters are selected to increase throughput performance; thus, the proposed method with \(\alpha=0.8\) and \(\beta=0.2\) produced the highest throughput performance. As \(\alpha\) decreases and \(\beta\) increases, the throughput performance of the proposed method becomes close to that of round-robin-based cluster selection. The simulation results also showed that the delay-based clustering performed better than the method without clustering. This is because transmission delay-based clustering increases channel use between the uplink data transmissions from stations and a block ACK transmission from an AP. The results also indicated that the proposed method provides better throughput performance than the other methods in a heavily dense network where a large number of stations is deployed for uplink transmissions.  
Figure 4: Network throughput performance (\(S=200\)).  
Figure 5: Fairness performance (\(S=200\)).  
Figure 5 shows the fairness performance with regard to the number of simultaneous uplink transmissions. The fairness performance was measured based on the amount of transmitted data of stations and calculated using [PERSON]'s fairness index. The results showed that transmission delay-based clustering with round-robin selection produced the highest fairness. This is because clusters are selected to transmit uplink data, and stations are fairly scheduled. On the other hand, proposed delay-based clustering with proportional fair selection shows lower fairness performance because clusters are selected to maximize throughput performance rather than fairness. However, as \(\alpha\) decreased and \(\beta\) increased, the fairness performance of the proposed method with proportional fair selection increased. The fairness performance of the proposed method with \(\alpha=0.5\) and \(\beta=0.5\) becomes similar to the fairness performance of the delay-based clustering method with round-robin selection when the number of simultaneous uplink transmissions is greater than or equal to six.  
Figure 6 shows the network throughput performance when there are 100 stations in the network. The throughput performance is similar to the results in Figure 4. Compared to the throughput performance results in Figure 4, the difference in throughput performance between the proposed delay-based clustering with proportional fair selection and delay-based clustering with round-robin selection decreases, especially when \(\alpha=0.5\) and \(\beta=0.5\). This is because as the number of stations decreases, the cluster candidates to be selected for uplink transmissions decrease. However, when \(\alpha=0.8\) and \(\beta=0.2\), the network throughput performance of the proposed method performs much better than the other methods. Note that the performance gain of the proposed method compared to the other method increases when a large number of stations are deployed in the networks.  
The simulation results showed that the proposed delay-based clustering with proportional fair selection enhances the network throughput performance of multi-user uplink transmission scenarios in IEEE 802.11 ax networks. In addition, by adjusting the proportionally fair parameters, \(\alpha\), and \(\beta\), the fairness performance would increase.