# New RED-Type TCP-AQM Algorithms Based on Beta Distribution Drop Functions
## 2 Description of the Problem and Related Works
Moreover, in [21], a new probability model with a variation of the packet drop function with respect to RED is proposed, obtaining an increase in throughput and a reduction in the expected end-to-end delay. There is a huge amount of research on the design of new dynamical AQM algorithms whose goal is to maintain a stable average queue length around a predetermined target under changing network traffic conditions. In fact, we can find recent work addressing the issue that show that the problem is still open. In [22; 23; 24; 25], the RED algorithm is modified in order to improve its performance and stability for various network states, obtaining better results compared to their predecessors. In [26], the Weight Queue Active Queue Management (WQDAQM) scheme, based on dynamic monitoring and reaction depending on the traffic load, is proposed. This algorithm aims to maintain the average queue length between two dynamically predetermined thresholds to prevent the buffer from exceeding the latter and overflowing. For our numerical comparison in Sections 4.3 and 5.3, we have chosen some representative AQM algorithms that are implemented in ns-3, such as Adaptive RED (ARED), Control Delay (CoDel) and Proportional Integral Controller Enhanced (PIE). We add a brief summary of the most important features of these algorithms as follows. ARED, proposed by [PERSON] et al. [27] and subsequently improved by [PERSON] et al. in [28], was intended to adjust the RED parameters adaptively to achieve a queue length around a prefixed target queue length. The main parameter that is tuned is the maximum packet drop probability, for which it uses an Additive-Increase-Multiplicative-Decrease (AIMD) approach. However, the performance of ARED is inferior to that of RED when faced with complex network environments. CoDel [29; 30] manages congestion control through the time that packets are in a given buffer (sojourn time), or the time a given packet spends in the queue of a buffer. Thus, CoDel distinguishes between a \"good queue\", one that does not show bufferbloat, maintaining an adequate delay in the face of bursts of traffic, and a \"bad queue\", one that, on the contrary, has a high buffer delay in the face of low utilization. PIE (see [31; 32; 33]) uses an estimate of the buffer queue delay as an indicator of congestion, marking with this estimated time each packet at the buffer entrance. When queuing a packet, a random discard is performed with a probability \(p\) obtained as a function of the latency calculated as an estimate of the delay and the trend that this value develops. PIE adopts the model Proportional Integral (PI) [34] to maintain the queuing delay at a specified target value. Furthermore, the algorithm self-adjusts the control parameters as a function of the level of congestion, directly reflecting this measure in the current discard probability, this being updated at regular intervals. The CoDel and PIE algorithms (see [32; 35], in which a comparative analysis is performed) are designed with the main objective of minimizing queue latency while maintaining high link utilization. They represent solutions to the problem raised in [36] of the Internet Engineering Task Force (IETF), where a call is made for the design of new methods to control network latency. For dumbbell topologies, both algorithms have performed well and mainly serve the purpose for which they were designed, which is to allow packet bursts to fill the buffer queue, preventing the queue from stalling under a persistent packet load.