## 2 Methods
### Reliable Transmission Design Mechanism
#### 2.1.2 NACK Dynamic Adjustment Transmission Mechanism
The parameter K used in the comparison algorithm (Algorithm 2), as mentioned in Section 2.1.2, was typically set to 1, while the parameter \(\alpha\) used by EWMA in Algorithm 5 was set to 13, with the multiplicative factor parameter x set to 0.5. The transmission waiting length L mentioned in the algorithm was the actual waiting time in the simulation, while avg was the predicted time, with an initial value of 0, which was calculated by the program in the subsequent simulation. The sending time of the out-of-order tolerance control affects the bandwidth usage caused by the Flow Completion Time (FCT) and false retransmissions. Therefore, it is very important to fit the real sending time. A waiting time that is too long increases the FCT, while a waiting time that is too short leads to false retransmissions. Although the FCT is an end-to-end concept, it can be inferred by accumulating values between nodes. In long flows, it is mainly related to the time of the last NACK transmission and the delay. We simulated and compared this in Figure 8. When looking solely at the FCT, the mean of the Fixed K Algorithm is smaller, which is an inevitable result of its slow convergence. When the delay suddenly increases, the NACK transmission time remains close to the previous result, but this approach causes an excessive number of false retransmissions, as shown in Figure 9; hence, it is not a good solution. Figure 7: Test topology. Therefore, we simulated some methods and compared their false retransmissions to further assess the effectiveness of our optimized link-local retransmission strategy. This comparison provided insights into the reduction in unnecessary retransmissions and the enhancement of network performance under various conditions. By simulating the packet disorder, we calculated the time for each NACK task to gather the packets and estimated the next time based on the previous times. We compared these algorithms for their prediction of sending times under the same environment, and the results are shown in Figure 10.

Figure 8: Mean FCT of different algorithms. Figure 9: False retransmission simulation. This method achieved better stability and lower false retransmission rates of around a quarter compared to other methods. Considering the above indicators, EWMA is indeed more suitable for this retransmission system. EWMA achieved better stability and a better fit and was more sensitive to changes in data. The fit of the Fixed K Algorithm relied heavily on the value of K, and the stability performance was poor. When the delay of each link was stable, the disorder also remained relatively stable. We set three different disorder conditions and simulated three aggregated links. The fitted curves are shown in Figure 11. The true time refers to the actual waiting time of this NACK, while the estimated time refers to the predicted time using the EWMA algorithm. It can be observed that this algorithm is capable of dynamically adjusting the sending time of NACKs. Figure 11: EWMA estimated time. Figure 10: RMSE of different algorithms. ### LL-ReTx Measurement of Real Packet Loss Scenarios

We continued utilizing the topology illustrated in \[N>\frac{log_{10}(target\_loss\_rate)}{log_{10}(actual\_loss\_rate)}-1 \tag{3}\]0 This configuration represents a real-world link where we deployed our Data Plane Development Kit (DPDK) program across two switches. In this setup, we intentionally enabled random packet loss on the network interface card to simulate adverse network conditions. Furthermore, we established multiple lines through routers, resulting in a total of 16 distinct lines. The data traffic was segmented into multiple streams as it traversed the intermediate router, allowing for a comprehensive analysis of network performance.