# A Sketch-Based Fine-Grained Proportional Integral Queue Management Method
## 2 Related Works
[13] proposed the delay control-based congestion control algorithm DX, which uses control theory to effectively reduce the queuing delay in the network while maintaining a high network throughput and ensuring good stability of the system. [PERSON] et al. [14] reconfigure the packet drop policy model based on the average queue-length change rate, effectively mitigating the delay jitter problem generated by network traffic changes. Another AQM technique [15] uses a semi-Markov decision process to estimate the probability of dropping an arriving packet before it enters the buffer but requires manual setting of the target delay for various network types. [PERSON] et al. [16] proposed an adaptive mechanism, multiplicative increase/reduction (MID), which minimizes the queuing delay by eliminating queues generated by AQM that depend on fixed targets, thereby achieving lower latency and jitter. [PERSON] et al. proposed ALTDROP [17], a random-drop adaptive queue management algorithm based on the average queue-size change rate, which can achieve better throughput in the presence of network congestion. [PERSON] et al. 2019 proposed high precision congestion control (HPCC) [18], which uses in-network telemetry (INT) to obtain accurate link load information and precisely control traffic. By dealing with the problems of delayed INT information and overreaction to INT information during congestion, HPCC can simultaneously achieve the three properties of ultralow latency, high bandwidth, and stability. [PERSON] et al. [19] used machine learning to create a model that replicates the behavior of the AQM mechanism, proposed a neural network-based AQM mechanism, and demonstrated its effectiveness. Refs. [20; 21] also proposed AQM algorithms based on neural networks. In the literature [22; 23], a mechanism based on neural network decision-making for selecting AQM parameters is proposed, utilizing a reinforcement learning approach. The literature [24] presents an improved AQM algorithm based on long short-term memory (LSTM) networks, leveraging LSTM's characteristics to predict and compensate for network delays, exhibiting good responsiveness in dynamic networks. In recent years, active queue management algorithms based on fuzzy logic control [25; 26] and optimization theory [27; 28] have been proposed. These AQM algorithms are designed for specific performance or specific scenarios of the network, determine the network state according to a scheme, and then apply the same drop policy to packets indiscriminately to relieve congestion, although they lack fine-grained differentiation between data streams and are unable to meet the performance requirements of both low latency and high fairness. Therefore, this paper proposes a Sketch-based proportional integral queue-management method based on the PIE algorithm, which first calculates the departure rate of packets in the queue buffer and the queue length, calculates the packet drop probability p based on this, and then uses the Sketch structure to judge the frequency count percentage of packets to identify large flows and makes targeted modifications to the packet drop probability of large flows in order to quickly alleviate network congestion based on a differentiated packet drop policy to ensure fairness among data flows, maintain network availability and stability, and improve the quality of service of the network.