## 4 Simulations
Packets whose deadline expired were removed from the arrival queue. 2. Packets with less than a 1-Kpbs rate did not begin transmission. 3. Packets were selected only from a window of \(K\) packets at the prefix of the queue. 4. All scheduling policies used ZFBF with a sequential insertion approach. 5. Matrices \(\mathbf{L}\) and \(\mathbf{Q}\) were downdated after packets ended their transmission. The naive implementation of FIFO, EDF, and priority greedy selects a packet from the head of the queue and waits until this packet has enough bandwidth to be transmitted. We first explore the possibility to allow these policies to look for an eligible packet out of the first \(K\) packets in the queue. We ran simulations with different window sizes \(K=\{1,2,4,6,8,10,12\}\) in order to set the appropriate window size. Figures 6-8 present the results of the number of delivered packets, the cumulative rewards, and the processing time using different values of \(K\), respectively. The results showed that  
Figure 5: Access point (red) and mobile station (blue) locations for 200 tests. increasing the window size improved the performance of the all policies while consuming more processing time. The RPS achieved an optimal performance already when \(K=2\). In other policies, the larger the window, the better the performance achieved, as well as the higher the CPU run time. In the subsequent simulations, we used a \(K=8\) in which FIFO, priority greedy, and RPS had a similar CPU consumption per packet. Figure 9 presents the cumulative reward of the different policies at different arrival rates. Figure 10 presents the number of packets that were delivered on time at different arrival rates. The general trend was as the traffic load became higher, less packets were delivered on time; however, the RPS packet loss was significantly lower than the other policies. In all measurements, the RPS policy outperformed significantly the other scheduling policies. Figures 11 and 12 present the overall simulation processing time and the average processing time per a delivered packet at different arrival rates. As expected, increasing the traffic load increased the processing time linearly. The processing time of FIFO, priority greedy, and RPS were similar. EDF showed worse performance. In Section 3, we present computational analysis of a single packet's handling. The results here emphasize that joint scheduling kept the overall performance low with less redundant processing time of packets that were not delivered on time. Figure 6: Percentage of delivered packets with different window sizes (\(\lambda_{a}=56\),000). Figure 7: Cumulative rewards’ percentage with different window sizes (\(\lambda_{a}=56\),000). Figure 8: Processing time in seconds with different window sizes (\(\lambda_{a}=\) 56,000). Figure 10: Percentage of delivered packets with different arrival rates. Figure 9: Percentage of cumulative reward with different arrival rates. Figures 13 and 14 present the CDF of the packets that were delivered on time. Figures 15 and 16 present the CDF of the cumulative reward. The 10% outage point at \(\lambda_{a}=\) 56,000 for RPS was 30% better than all other scheduling policies, both in the cumulative reward and in the number of delivered packets. As the arrival rate was higher, all policies collected less rewards and delivered less packets on time. The degradation of the service was not similar for all policies; the FIFO policy suffered the most; the EDF policy and the priority greedy policies suffered less; while the RPS policy had a minor degradation of the performance. The RPS policy cumulative reward was 35% better at a 10% outage than the priority greedy policy and was 40% better than the priority greedy policy in the expected total number of delivered packets. One should note that the RPS policy also provided a significantly more robust packet delivery, since the expected reward CDF was very concentrated compared to the other scheduling policies. Figure 11: Processing time in seconds with different arrival rates.