# Transmission Delay-Based Uplink Multi-User Scheduling in IEEE 802.11 ax Networks +
## 5 Proportional Fair-Based Transmission Scheduling  
### Clustering-Based Proportional Fair Schedular  
In the proposed method, stations are first clustered on the basis of transmission delay, and then the AP schedules clusters to transmit uplink data. Note that stations with similar transmission delays are clustered together to enhance channel use and network throughput performance in the uplink multi-user scenario. With highly efficient clusters  
Figure 3: Normalized channel use (packet arrival rate and transmission rate are same. There are 24 non-AP stations.  
Figure 2: Normalized channel use (packet arrival rate and transmission rate are same). There are 16 non-AP stations.  
for the uplink multi-user transmission scenario in IEEE 802.11 ax networks, we propose a cluster scheduling method on the basis of a proportional fair-based approach. Proportionally fair scheduling enhances network throughput as well as the fairness of stations trying to transmit data by adjusting the priority of stations inversely proportional to their previous resource consumption. The proportional fair-based method is one of the widely used scheduling approaches, because it can achieve good performance both in network throughput and fairness among stations. In the proposed method, higher transmission opportunity can be achieved, as stations are starving to transmit uplink data and have shorter transmission delays.  
The proposed method performs scheduling after the stations are clustered together on the basis of their transmission delays as in (3). Let \(v^{t}_{c^{t}_{l}l}\) be the proportional fairness value of cluster \(l\) (\(C^{t}_{l}l\subset\mathcal{C}^{t}\)) at time slot \(t\). We denote the transmission rates of station \(s_{i}\), \(s_{i}\in\mathcal{S}\) at time slot \(t\) as \(R^{t}_{s_{i}}(\gamma_{a,s_{i}})\). In this paper, we define proportional fairness on the basis of transmission delay, so that uplink multi-user transmission delay is minimized in IEEE 802.11 ax networks. The proposed proportional fairness value of each cluster is defined as follows:  
\[v^{t}_{c^{t}_{l}l}=\frac{\{\sum_{s_{i}\in C^{t}_{l}l}R^{t}_{s_{i}}(\gamma_{a,s _{i}})^{-1}\}^{\alpha}}{\{\frac{1}{\prod_{k=l-T}^{t-1}\sum_{s_{i}\in C^{t}_{l} l}R^{k}_{s_{i}}(\gamma_{a,s_{i}})^{-1}\}^{\beta}}}\enspace, \tag{4}\]  
where \(\alpha\) and \(\beta\) are the adjustment values for balancing transmission delay and fairness performance, respectively. For example, for \(\alpha=1\) and \(\beta=0\), the proportional fairness value is the sum of transmission delays of stations in the cluster. On the other hand, for \(\alpha=0\) and \(\beta=1\), clusters are scheduled in a round-robin manner. Note that the averaging duration \(T\) is adjustable within the hardware limitations.  
In the proposed method, proportional fairness value of all clusters in \(\mathcal{C}^{t}\) is calculated at every scheduling period, and the cluster with the minimum value is scheduled for uplink data transmission. The cluster scheduling problem for multi-user uplink transmissions at time \(t\) is formulated as follows:  
\[\underset{c^{t}_{l}l\in\mathcal{C}^{t}\text{min}}{\arg\min}\;v^{t}_{c^{t}_{l} l}. \tag{5}\]  
Equation (5) can be easily solved by comparing the proportional fairness value of clusters in \(\mathcal{C}^{t}\). After finding the cluster with the minimum value, the stations in the selected cluster are scheduled for simultaneous uplink multi-user transmissions. Note that the proposed scheduling method efficiently enhances uplink channel use and network throughput performance by clustering stations with similar transmission delays and avoids the channel access starving of stations by exploiting proportional fairness.