# New RED-Type TCP-AQM Algorithms Based on Beta Distribution Drop Functions
## 2 Description of the Problem and Related Works  
Numerous AQM algorithms with different approaches have been proposed over the past two decades to handle the queuing delay problem. However, the conditions of a network and the specific user needs may vary from one scenario to another, so there is no algorithm that can satisfy all demands at the same time. In addition, the optimal configuration of the parameters involved in this type of algorithm is complicated. This is why no single AQM has had a predominant deployment over the others, and the AQM that obtains the best performance in the given scenario is selected. This fact is what has most negatively affected the widespread application of the RED mechanism. There are a large number of publications in the literature aimed at overcoming these difficulties by variations on the RED algorithm. A good summary can be found in [15], which in turn contains a large collection of citations of work based on RED technology. However, the problem is still topical and we can find numerous recent works addressing the issue. Drop Tail is the simplest algorithm that can be designed: the buffer accepts packets until it is completely full, and when this happens, it discards the last packets received. The main problem with this mechanism is its performance when combined with TCP, which reduces the sending rate when it receives packet loss notifications, and this occurs only after the buffer is completely full. This, in turn, causes TCP to generate a flow with intermittent bursts, which, with full buffers, causes packet loss to increase in each Round \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**AQM Algorithm** & **Name** & **Description** \\ \hline \multirow{6}{*}{\
\begin{tabular}{} \end{tabular} } & ABetaRED, & \(T_{\text{target}}\) & Target delay \\ \cline{2-4}  & DBetaRED, ARED, & \(T_{\text{update}}\) & Update interval time \\ \cline{2-4}  & CoDel, PIE & Alpha, Beta & Control parameters with different objectives according to the AQM. \\ \cline{2-4}  & BetaRED, ABetaRED & \(\theta\) & \(\frac{\text{Scale factor determining the standard deviation of the drop probability function}}{\text{$w$}}\) & \(\text{Average weight}\) \\ \cline{2-4}  & BetaRED & \(q_{\text{target}}\) & Target queue length \\ \cline{2-4}  & BetaRED & \(q_{\text{min}}\) & Lower threshold \\ \cline{2-4}  & & \(q_{\text{max}}\) & Upper threshold \\ \cline{2-4}  & & \(p_{\text{max}}\) & Maximum packet drop probability \\ \hline \multirow{6}{*}{
\begin{tabular}{} \end{tabular} } & & \(B\) & Buffer size (maximum number of packets that the buffer of Router 1 can store) \\ \cline{2-4}  & All & \(C\) & Capacity of the channel (the maximum amount of error-free information that can be transmitted over the channel per unit time) \\ \cline{2-4}  & & \(N\) & Number of flows in the dumbbell topology \\ \cline{2-4}  & & \(M\) & Packet size \\ \cline{2-4}  & & \(p\) & Drop probability \\ \cline{2-4}  & All & \(q_{\text{cur}}\) & Current queue length at Router 1 \\ \cline{2-4}  & & \(q_{\text{avg}}\) & Average queue length at Router 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notation for the most important parameters and variables used throughout the paper. Trip Time (RTT) cycle, eventually ending up in a degraded circular dynamics with high latency and low throughput. The problem is further aggravated when the number of flows connected in the same link increases, each regulated by its own congestion window. It has been found that, in this situation, the slow start of each of the flows tends to synchronize, causing the phenomenon known as global synchronization [4], which is characterized by very low overall network throughput. Active queue management attempts to provide a solution to problems that appear in Drop Tail (see [5; 16]) by notifying congestion initiation signals before the buffer fills up. Notification can be done via packet drop or with the Explicit Congestion Notification (ECN) flag.