# Transmission Delay-Based Uplink Multi-User Scheduling in IEEE 802.11 ax Networks +
## 2 Related Work
### Proportional Fair-Based Scheduling  
Proportional fairness is widely used because of its efficiency in improving both throughput and fairness performance. [PERSON] and [PERSON] analyzed the throughput and fairness performance of scheduling methods, including proportional fair-based scheduling [17]. Through the numerical analysis, the authors showed that the proportional fair-based scheduling method provides relatively better trade-offs between throughput and fairness compared to the round-robin and maximum carrier-to-interference ratio scheduling methods. [PERSON] and [PERSON] studied the proportional fair-based rate allocation problem in IEEE 802.11 networks [18]. Within the possible achievable rate region, they proposed a rate allocation method on the basis of air time information. Under some assumptions, such as interference is limited and stations are backlogged, the proportional fair-based rate allocation showed optimal performance in IEEE 802.11 networks. The proportional fairness-based user scheduling approach has been studied in MU-MIMO or OFDMA systems. [PERSON] et al. studied proactive proportional fairness scheduling based on channel prediction in OFDMA systems [19]. Using the predicted channel information, they proposed a proportional fair-based resource allocation method. Their findings showed that proportional fairness-based scheduling has the potential to improve network performance combined with other techniques such as channel predictions. [PERSON] et al. studied deep reinforcement learning based resource allocation and a power control method with proportional fairness in device-to-device communications [20]. In the proposed method, utility function for proportional fairness of device-to-device pairs is used for resource allocation.  
In this study, we used the proportional fair-based scheduling approach to further improve the performance of our previously reported method. Our previous work shows that transmission delay-based scheduling improves the throughput performance in IEEE 802.11 ax networks [21]. In the transmission delay-based scheduling method, stations with similar transmission delays are clustered together to simultaneously transmit uplinkdata. By scheduling stations with similar transmission delays, the channels can be efficiently utilized in the uplink multi-user transmission scenario in IEEE 802.11 ax networks. We further improved the transmission delay-based scheduling method so that the proposed method would show good throughput performance in a network with a large number of stations. We applied a proportional fair-based approach in the transmission delay-based scheduling method to efficiently improve throughput performance while maintaining good fairness among the stations. After the transmission delay-based station clustering, a clustering-based proportional fair approach is adopted to select clusters for uplink multi-user transmissions. The proposed method also performs re-clustering so that differences in transmission delays of stations do not significantly increase, resulting in low channel use.  
Through the various IEEE 802.11-compliant simulations and SDR-based experiments, we show the feasibility of the proposed scheduling method in IEEE 802.11 ax networks.