# Transmission Delay-Based Uplink Multi-User Scheduling in IEEE 802.11 ax Networks +
## 4 Transmission Delay-Based Station Clustering
### Numerical Analysis of Channel Use  
In this section, we present the channel use efficiency of the proposed transmission delay-based station clustering. The proposed station clustering method improves the uplink channel use of multi-user transmissions following the scenarios specified in IEEE 802.11 ax. On the basis of the CSI and BSR from stations trying to participate in uplink multi-user transmissions, the expected transmission delay of each station is calculated. Then, the stations with similar transmission delays are clustered together for simultaneous uplink transmissions. We analyzed the performance of the proposed transmission delay-based station clustering, and show that the proposed method improves the channel use of uplink multi-user transmissions in IEEE 802.11 ax. To prove the concept of transmission delay-based station clustering, we compare the normalized channel use through simulations with a simplified toy model. In the toy model, the PPDU size of a single frame is uniformly distributed, and information about the transmission delays of stations is assumed to be known for the clustering method described in Section 4.1. We define the normalized channel use as the average transmission delay normalized by the maximum one among the selected stations. In this simulation, the transmission rates of stations selected for uplink transmissions are all assumed to be the same, and packet arrival rates follow the Poisson distribution. Note that if the transmission rates are all the same for the selected stations for uplink multi-user transmissions, the PPDU size is directly related to the transmission delay. Hence, if all the uplink PPDU sizes of the selected stations are the same, the normalized channel use is 1. As the normalized channel use approaches 1, channels become less underutilized during the time between the end of the PPDU transmissions and the start of block ACK transmission. We compare the channel use of the transmission delay-based clustering method with periodic re-clustering, transmission delay-based clustering method without re-clustering, and the random selection method. In the simulations, the number of simultaneous uplink transmissions was set to 8, i.e., 8 stations were selected. Figure 2 shows the channel use results regarding transmission time when 8 out of 16 stations were selected for uplink transmissions. From the results, transmission delay-based station clustering shows higher channel use performance than the random selection method. However, the performance of the transmission delay-based clustering method without re-clustering degrades over time, while the random selection method shows consistent channel use performance. This is because the transmission delay changes over time according to the transmission environments, such as packet arrival rates or transmission rates. To compensate for the changes in transmission environments, stations should be re-clustered based on expected transmission delays. The transmission delay-based clustering method with re-clustering performs station clustering every 5 times, and it shows better channel use performance compared than the other methods. Figure 3 shows the channel use results with regard to transmission time when there are 24 stations. The simulations result is similar to the one shown in Figure 2, but it indicates that re-clustering becomes more important in the network with many stations. Note that transmission delay calculations need the BSR and CSI from stations trying to participate in uplink multi-user transmissions. Hence, performing station clustering every transmission increases overhead, and the throughput performance may degrade. Through the concept-proof simulations, we show that the transmission delay-based station clustering can improve channel use, which is directly related to the network throughput performance. We also show that re-clustering should be performed for the station clustering-based method to follow the changes in uplink transmission environments.