# New RED-Type TCP-AQM Algorithms Based on Beta Distribution Drop Functions
## 5 Dynamic Algorithms Based on BetaRED
### Simulations  
This section presents the results and discussion of the numerical simulations performed to compare ABetaRED (Section 5.1) and DBetaRED (Section 5.2), as well as these algorithms with the selection of the other AQM algorithms described in Section 2. The simulations are performed in several scenarios according to different parameters and levels of congestion, including slight, moderate and abrupt variations in the number of nodes in order to verify the robustness of the proposed AQM algorithms. However, space limitation conditions us to present only a selection of the most important features regarding the behavior of the above algorithms. The first comparison we carried out was between the ABetaRED and DBetaRED algorithms (see Figures 5 and 6) when we progressively increase the parameter \(\theta\) (and hence the standard deviation \(\sigma\)). Figure 5 shows the result of the simulations for a constant level of congestion (Scenario 1 described in Section 3.1), while Figure 6 shows the result for a changing level of congestion (Scenario 2 described in Section 3.1). It is observed that, in both algorithms, the throughput is quite unpredictable for different \(\theta\) parameters. However, the jitter is lower the smaller the value of the \(\theta\) parameter, i.e., for smaller \(\sigma\) values. Figure 5: Comparison between ABetaRED and DBetaRED algorithms according to the standard deviation \(\sigma\). Different levels of congestion are also considered by means of a constant number \(N\) of active flows. Other tuning parameters: \(T_{\text{target}}=40\,\text{ms}\) (\(q_{\text{target}}=250\) packets) and \(w=0.1\). Scenario 1 on the dumbbell topology (described in Section 3.1) is used. Overall, the DBetaRED algorithm exhibits better performance, especially for the end-to-end jitter metric. Figure 7 shows the performance of DBetaRED for different levels of congestion according to different values of the weight parameter \(w\). It can be seen that whatever the level of congestion, the choice of a sufficiently high \(w\) parameter guarantees a satisfactory performance. However, the most appropriate value of \(w\) according to the scenario is difficult to estimate, as it may vary depending on the network topology, the level of congestion, etc. In any case, it was observed that the qualitative behavior does not change from one scenario to another. Figure 6: Comparison between the ABetaRED and DBetaRED algorithms according to the parameter \(\theta\). Different levels of congestion are also considered, but, unlike in Figure 5, the number \(N\) of active flows varies dynamically with time. Other tuning parameters: \(T_{\text{target}}=40\,\text{ms}\) (\(q_{\text{target}}=250\,\text{packets}\)) and \(w=0.1\). Scenario 2 on the dumbbell topology (described in Section 3.1) is used. As in the non-dynamic scenario (Figure 5), the DBetaRED algorithm performs better than the ABetaRED algorithm. It is of special interest when a comparison is made with other related AQM schemes. The common denominator of all the selected dynamic algorithms to be compared with ABetaRED and DBetaRED is the need to set the target delay parameter \(T_{\text{target}}\). However, the mechanism of action of each of the AQM algorithms according to this parameter is different. CoDel starts dropping packets when the queue delay remains above the target delay for a certain time. PIE continuously updates its probability of dropping packets according to the difference between the current queue delay and the target delay. ARED does not act directly as a function of the target delay, but rather as a function of a target queue length estimated via the target delay. Both ABetaRED and DBetaRED algorithms act in the same way as ARED, namely, to achive a given predetermined \(T_{\text{target}}\), a target queue length given by \(q_{\text{target}}=C\cdot T_{\text{target}}\) is estimated, where \(C\) is measured in packets per second.