## 2 Methods
### Reliable Transmission Design Mechanism
#### 2.1.2 NACK Dynamic Adjustment Transmission Mechanism
Moreover, our findings highlight the importance of considering both data packets and control signals, such as ACKs and NACKs, in the calculation of bandwidth utilization. By optimizing the retransmission process and minimizing spurious retransmissions, we achieved a high bandwidth utilization rate, even under significant packet loss conditions. This not only enhances the efficiency of the network but also ensures that real-time applications, which are sensitive to delays, disruptions, and bandwidth fluctuations, can operate smoothly. In conclusion, we believe that our proposed solution is highly valuable for WANs. By addressing the challenges posed by packet loss and link corruption, we contribute to the development of more resilient and efficient networking solutions, ultimately enhancing the quality of service for users and applications that rely on stable and high-performance network connections. Future work will focus on further refining the feedback mechanisms and switch architecture design to predict and adapt to dynamically changing network conditions. Conceptualization, L.S. ; methodology, implementation, and validation, C.K. and Y.L. ; writing--original draft preparation, C.K. ; writing--review and editing, L.S. and C.K. ; supervision, L.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development Program of China: Demonstration of Multimodal Network Application for Eastern Data and Western Computing (Project. No. 2023 YFB2906404). All the necessary data are included in the article. The authors would like to extend their sincere gratitude to [PERSON], [PERSON], and [PERSON] for their insightful comments. Additionally, the authors are deeply appreciative of the anonymous reviewers for their constructive feedback on the earlier drafts of this manuscript. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} WAN & Wide-Area Network \\ RDMA & Remote Direct Memory Access \\ NPA & Network Performance Anomaly \\ TCP & Transmission Control Protocol \\ SACK & Selective Acknowledgment \\ ECN & Explicit Congestion Notification \\ FEC & Forward Error Correction \\ DCN & Data Center Network \\ LSN & Low-Earth-Orbit (LEO) Satellite Network \\ HPC & High-Performance Computing \\ ARQ & Automatic Repeat Request \\ FRER & Frame Elimination for Reliability \\ FPGA & Field-Programmable Gate Array \\ LL-ReTx & Link-Local Retransmissions \\ FCT & Flow Completion Time \\ SQR & Shared Queue Ring \\ DPDK & Data Plane Development Kit \\ NACK & Negative Acknowledgment \\ RMSE & Root Mean Square Error \\ EWMA & Exponentially Weighted Moving Average \\ SDN & Software-Defined Networking \\ MTU & Maximum Transmission Unit \\ \end{tabular} 

## References

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