## 7 Performance Evaluation
### Simulation Results and Discussions
#### 7.3.4 EDF, DRRF, and EDF-DRRF  
We show system throughput, delay, and delay jitter of EDF, DRRF, and EDF-DRRF with deadline enforcement. For the first scenario (under-load scenario), all three algorithms result in the same throughput, 1.5, 1.24, and 1.49 Mbps with 1.19 Mbps with CBR. There are no dropped packets for video flows. The average delay ranges from 6 to 7 ms.  
Table 7 shows the results for the second overload scenario with deadline enforcement. Because of the deadline enforced, average delays for all three algorithms are within the specified deadline of 20 ms plus 5 ms additional transmission delays (duration of the WiMAX frame). EDF is unfair,  
Figure 7: DRRF Throughput. a. (left) with 5 flows: \(MS_{I}\) with 500 kbps \(r_{max}\); b. (right) 5 flows: \(MS_{I}\)_and \(MS_{I}\)_with traffic priority 2 and \(MS_{I}\) to \(MS_{I}\)with traffic priority 1 [10].  
while DRR and EDF-DRRF are fair. The degree of fairness of DRRF is a bit higher than EDF-DRRF, 0.9998 _versus_ 0.9986, respectively.  
Table 8 shows the results for the case with one ill-behaved flow. Deadline is enforced for all flows. Again, EDF cannot maintain the share for well-behaved flows. On the other hand, DRRF and EDF-DRRF can achieve max-min fairness for all flows.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Mobile Station** & **Sender (Mbps)** & **Receive (Mbps)** & **Delay (ms)** & **Delay Jitter (ms)** \\ \hline (a) EDF & & & & \\ \hline
1 & 1.49 & 0.90 & 21.38 & 1.80 \\
2 & 1.18 & 0.76 & 20.83 & 2.07 \\
3 & 1.53 & 1.14 & 21.31 & 1.79 \\
4 & 1.24 & 0.74 & 21.22 & 1.83 \\
5 & 1.47 & 1.11 & 21.20 & 1.75 \\ \hline (b) DRRF & & & & \\ \hline
1 & 1.49 & 0.95 & 18.65 & 3.84 \\
2 & 1.18 & 0.98 & 16.27 & 4.30 \\
3 & 1.53 & 0.96 & 19.03 & 3.46 \\
4 & 1.24 & 0.97 & 16.91 & 4.31 \\
5 & 1.47 & 0.98 & 18.28 & 3.86 \\ \hline (c) EDF-DRRF & & & & \\ \hline
1 & 1.49 & 0.89 & 19.63 & 3.08 \\
2 & 1.18 & 0.95 & 17.07 & 4.26 \\
3 & 1.53 & 0.85 & 19.90 & 3.24 \\
4 & 1.24 & 0.89 & 18.04 & 4.04 \\
5 & 1.47 & 0.88 & 19.63 & 3.06 \\ \hline \end{tabular}
\end{table}
Table 7: System Throughput, Delay, and Delay Jitter with Deadline Enforced (5 Flows in Overload Scenario) (a) EDF, (b) DRRF, and (c) EDF-DRRF [13].  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Mobile Station** & **Send (Mbps)** & **Receive (Mbps)** & **Delay (ms)** & **Delay Jitter (ms)** \\ \hline (a) EDF & & & & \\ \hline
1 & 1.49 & 1.19 & 20.41 & 1.93 \\
2 & 1.24 & 1.03 & 20.16 & 1.99 \\
3 & 3.33 & 2.66 & 21.28 & 1.83 \\ \hline (b) DRRF & & & & \\ \hline
1 & 1.49 & 1.49 & 9.69 & 3.33 \\
2 & 1.24 & 1.24 & 8.70 & 3.05 \\
3 & 3.33 & 2.34 & 20.58 & 2.87 \\ \hline (c) EDF-DRRF & & & & \\ \hline
1 & 1.49 & 1.49 & 9.80 & 3.72 \\
2 & 1.24 & 1.24 & 9.07 & 3.41 \\
3 & 3.33 & 2.34 & 20.62 & 2.77 \\ \hline \end{tabular}
\end{table}
Table 8: System Throughput, Delay, and Delay Jitter with Enforced Deadline: 2 Well-Behaved Flows and 1 Ill-Behaved Flow in Overload Scenario (a) EDF, (b) DRRF, and (c) EDF-DRRF [13].  
The results in Tables 7 and 8 follow the theoretical expectation in that EDF with a hard deadline constraint dominates the resources resulting in other flows to starve and their packets to be dropped because video traffic is bursty in its nature. Hence, the number of the dropped packets in the EDF scheme is higher than in the other schemes. Bursty packets with deadline constraints results in larger delays for packets in other queues.  
Consider delay jitter. Since we use bursty traffic which allows a group of continuous packets to be passed in a short time, the results show in a smaller delay jitter value. In comparing DRR and EDF-DRRF, in EDF-DRRF the bursty nature of the traffic restricts the influence of EDF, and allow more dominance of DRRF that results in similar values to the one obtained by using DRRF.