# A Sketch-Based Fine-Grained Proportional Integral Queue Management Method
## 3 System Model
### Queue Management
A proactive packet drop means that when the number of packets in the network exceeds the processing capacity of the network and, thus, causes network congestion, packets are dropped proactively to relieve congestion. On the other hand, passive packet drop is a reactive strategy. When a passive packet drop occurs, the buffer of the network node is full, and the network is in a state of extreme congestion. Excessive passive packet drops can lead to unstable data transmission and degradation of the network performance; therefore, it is important to reduce passive packet drops. From Figure 10a, it can be observed that S-PIE reduces the passive packet drop significantly compared to PIE by approximately 83.41%. There is no passive packet drop in RED because RED actively drops packets based on judging the average queue length with respect to the threshold value, and packets are dropped when the average captain exceeds the set maximum threshold value. Therefore, in this experimental scenario, RED's captain basically does not exceed the maximum number of packets allowed in the buffer and, thus, does not generate passive packet loss. Figure 10b shows the active packet drop of each algorithm, which illustrates that each AQM algorithm identifies the extent of network

Figure 10: Comparison of packet drops (Scenario 2). Figure 9: Comparison of the fairness index in different scenarios. congestion leading to an autonomous packet drop. As can be seen from the figure, in the presence of network congestion, combined with the previous comparison of throughput and average queue-length performance, S-PIE can better predict congestion for active packet drops and penalize packet drops for large flows to maintain fairness among data flows and effectively mitigate congestion. ## 5 Conclusions

In this study, we propose a fine-grained proportional integral queue management method, S-PIE, based on Sketch. S-PIE can count the frequency of the corresponding flow of packets through the Sketch module and determine whether the flow is a large flow according to the frequency statistics, so as to perform differential packet drop to ensure fairness, and the memory cleaning module can prevent Sketch memory overflow. The experimental results show that the S-PIE algorithm achieves a lower average queue length, RTT, and higher fairness while maintaining a similar throughput performance compared to the original algorithms RED, CoDel, and PIE. The S-PIE framework implements a differential packet drop policy to ensure the fairness of data flows, maintain network availability and stability, and improve network quality of service by maintaining shorter queue lengths. In the future, we will continue to study the S-PIE algorithm in more complex real network environments (rather than simulated experimental environments) to increase its generality, and new developments related to Sketch can help us further improve the performance of the S-PIE algorithm. Conceptualization, H.Z. and H.S. ; methodology, H.Z. and G.H. ; writing--original draft preparation, H.S. and Y.J. ; writing--review and editing, L.Z. and Y.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (Grant No. 62272237, 52105553, 71801123) and the Key Projects of Natural Science Research in Jiangsu Provincial Colleges and Universities under Grant 22 KJA520005. Not applicable. The authors declare no conflict of interest. ## References

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