## 2 Methods
### Reliable Transmission Design Mechanism
#### 2.1.2 NACK Dynamic Adjustment Transmission Mechanism
The one-way propagation delay was measured to be 40 ms. As illustrated in Figure 12, it is evident that under the specific conditions of transmitting four negative acknowledgment (NACK) messages and subsequently retransmitting three data packets, the system demonstrated a remarkable ability to mitigate packet loss. With a real link packet loss rate maintained at a high 1% loss rate, the actual effective packet loss rate was reduced to an impressive extent, achieving a reduction of at least three orders of magnitude. The algorithm we used achieved good bandwidth utilization when the packet loss rate was below a certain magnitude. We observed that the length of the extra header bytes for ACKs or NACKs containing the necessary information was about one-hundredth of the maximum transmission unit (MTU). Considering the median packet size of 256 B observed in networks [28], Table 2 shows the bandwidth utilization calculated based on this parameter. We take into account the proportion of packets that were false retransmissions and the proportion of bandwidth used by NACKs and ACKs. The parameters were set according to the ratio of the false retransmission rate of the 3.1 simulation, which was nearly a quarter. \begin{table}
\begin{tabular}{c c c} \hline  & **Our Work** & **LinkGuardian [26]** \\ \hline Utilization (loss rate = \(\alpha\), count = n, & \(1/(1+\text{n}\alpha\beta+\text{m}\alpha)\) & \(1/(1+\text{n}(1-\alpha)\beta+1.25\text{ m}\alpha)\) \\ retrans = m, length ratio = \(\beta\)) & & \\ \((10^{-2},5,3,1/100)\) & 96.9\% & 87.9\% \\ \((10^{-2},10,3,1/100)\) & 96.9\% & 84.3\% \\ \((10^{-2},15,3,1/100)\) & 96.8\% & 80.9\% \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of theoretical values of bandwidth utilization. Figure 12: Effective packet loss rate. We deployed our program on the nodes of a real-world long-distance transport network, whose topology is shown in Figure 13.

We compared the transmission efficiency of our solution with that of traditional technologies in a real-world WAN environment, as shown in Table 3. At a distance of about 500 km and a packet loss rate of 1/1000 at 10 Gbps throughput, our approach maintained 76.8% of the network throughput, while the traditional TCP protocol, the Cubic algorithm, dropped to 0.30% of the network throughput, and the traditional RDMA technology dropped to 0.30% of the network throughput. The transmission efficiency of our approach was 256 times higher than that of the traditional TCP protocol and 256 times higher than that of the traditional RDMA technology, while the utilization rate of the entire network link increased to 77%. ## 4 Discussion

### Comparison with the Existing Literature

Our program has been running stably in the experimental environment for a long time. The reduction in the packet loss rate is inherently linked to the number of retransmissions, a concept discussed in Section 2.2.4 and further supported by the findings in Section 3.2. Our results align with those from other studies; for instance, Link Guardian [26] demonstrated a reduction from a \(10^{-3}\) packet loss rate to a \(10^{-6}\) rate through two retransmissions. In comparison to existing link-layer retransmission mechanisms and algorithms, our approach excels in managing out-of-order packets, which are known to trigger false retransmissions and excessive waiting times. As detailed in Section 3.1, our simulations replicated the mechanisms used in other studies, including LinkGuardian [26]. Our mechanism, which includes processing for out-of-order packets, outperformed these mechanisms, reducing false retransmissions by 25%. Moreover, our NACK-based transmission strategy provided superior link utilization, as indicated in Table 2, by conserving resources and reducing overhead. Additionally, Table 3 illustrates that our solution mitigated the dramatic decrease in throughput caused by packet loss for various protocols on the devices discussed in the introduction.