# New RED-Type TCP-AQM Algorithms Based on Beta Distribution Drop Functions
## 6 Conclusions  
In this work we propose new RED-type AQM algorithms, which we call BetaRED, ABetaRED and DBetaRED. Using a simple dumbbell topology and applying different levels of congestion (both constant and variable), we have analyzed and evaluated its performance comparing it with the ARED, CoDel and PIE algorithms through different performance metrics such as the average queue length, the packet queue rate, the end-to-end throughput, the end-to-end delay (latency) and the delay jitter. We have shown that the new BetaRED algorithm is a simple, flexible and robust mechanism, which provides good stability and performance over a very wide range of parameters. However, BetaRED needs parameter tuning according to the network characteristics and congestion scenario. In order to reduce the number of tuning parameters, the dynamic algorithms ABetaRED and DBetaRED (based on BetaRED) have been proposed and compared with benchmark algorithms such as ARED, CoDel and PIE, obtaining comparable results and even outperforming them in certain scenarios. DBetaRED stabilizes queueing length, further improves throughput and reduces packet drops, compared to other representative AQM algorithms, most notably in high-load congestion scenarios. Although the simulations carried out to obtain these conclusions have been numerous, the testing possibilities are enormous, and so there is still a lot of work to be done in this regard. Additionally, we share the view of [39] that the choice of the TCP-AQM couple to  
Figure 9: Stability comparison between related AQM algorithms when considering different levels of congestion by varying dynamically the number \(N\) of active flows with \(N_{\text{max}}=800\). Other tuning parameters: \(7_{\text{target}}=40\,\text{ms}\) for all AQM algorithms; \(\theta=0.1\) and \(w=0.1\) for ABetaRED and DBetaRED. Scenario 2 on the dumbbell topology (described in Section 3.1) is used. The bottom right panel shows a comparison of the average queue length (for the total simulation time) of all selected AQM algorithms. The other panels illustrate the instantaneous queue length pattern, together with its moving average queue length (of the last 25 s) for each of the AQM algorithms. Among all the algorithms, DBetaRED exhibits the highest stability. adopt is crucial, i.e., the most effective congestion control would occur when AQM and TCP work together in a shared bottleneck. Consequently, we continue studying heterogeneous scenarios of our AQM algorithms with variants of TCP different to those studied in this paper. Specially, it would be interesting to evaluate the behavior of the proposed AQM algorithms with the bottleneck bandwidth and round-trip time (BBR) congestion control algorithm published by Google in 2016. Unlike packet loss-based TCP variants (such as Cubic and Reno), BBR is designed to obtain a high performance coupled with low bottleneck buffer occupancy, reducing packet loss and minimizing delay by means of its end-to-end action. Thus, the effect of the proposed AQM algorithms is likely to be negligible in this case, or even negatively affect overall performance. Last but not least, the proposed BetaRED-type algorithms are not claimed to provide a general optimal solution, since the optimality of the parameters will depend on the objective set and the characteristics of the scenarios. Therefore, one of our future research topics will be the search for optimal settings of BetaRED parameters in different concrete network scenarios, for which an in-depth analysis of mathematical models derived from the BetaRED algorithm will be necessary. Conceptualization, A.G., M.A.M., J.M.A., O.M.-B. and J.V. ; methodology, A.G., M.A.M. and O.M.-B. ; software, A.G.and M.A.M. ; writing--review, A.G., M.A.M., J.M.A., O.M.-B. and J.V. ; content discussion and final version, A.G., M.A.M., J.M.A., O.M.-B. and J.V. All authors have read and agreed to the published version of the manuscript.