## 4 Problem Modeling and Solution
### Logical Topologies Construction
As a result, the RANK method provides shorter paths under low-traffic conditions, thereby reducing average packet delay, and helps alleviate congestion in high-traffic conditions. #### 5.3.2 Average Packet Loss Rate

Figure 5 shows the impact of the four methods on the average packet loss rate when the device moves to S1. Figure 4: Comparison of average packet delay among different methods with the increasing number of flows: (**a**) when the device moves to S10; (**b**) when the device moves to S12. Figure 5: Comparison of average packet loss rate among different methods with the increasing number of flows when the device moves to S1. When the number of data flows is between 5 and 10, all four methods provide paths that can accommodate all data flows without congestion, resulting in a packet loss rate of 0. As the number of data flows increases to 15, the AMPLE method experiences congestion, causing the average packet loss rate to rise to 0.19. When the number of data flows reaches 20, the single-path method becomes congested, and the average packet loss rate increases to 0.22. As the number of data flows grows to 35, the k-shortest method also experiences congestion, with the average packet loss rate rising to 0.14. Throughout the experiment, the RANK method consistently provides sufficient paths for mobile data flows, effectively avoiding congestion and maintaining a packet loss rate of 0. Figure 6a shows the performance of the four methods on the average packet loss rate when the device moves to S10. Similar to the previous case, the RANK method experienced no congestion throughout the experiment, maintaining a packet loss rate of 0. Figure 6b shows the performance of the four methods on the average packet loss rate when the device moves to S12. When the number of data flows is between 5 and 30, the RANK method performs well, maintaining a packet loss rate of 0. As the number of data flows increases to 35, the RANK method experiences congestion, but the level of congestion is lower compared to the other three methods. The average packet loss rate for RANK is 0.18, which is 48% lower than k-shortest, 53% lower than AMPLE, and 72% lower than the single-path method. Overall, the RANK method performs the best in terms of the average packet loss rate. As the number of flows increases, RANK continues to provide paths that can accommodate all the flows, thereby maintaining a stable packet loss rate of 0. Even when traffic reaches levels that cause congestion, the RANK method mitigates congestion severity by providing distinct paths that avoid overlap on bottleneck links. The RANK method effectively reduces congestion, leading to a significantly lower average packet loss rate. #### 5.3.3 Throughput

Figure 7 illustrates the impact of the four methods on throughput when the device moves to S1, S10, and S12. From the figure, it is evident that regardless of the device's location, the RANK method provides the highest transmission capacity, resulting in the highest throughput compared to the other three methods. Specifically, when the device moves to S1, the throughput achieved by the RANK method reaches 26.32 Mbps, which is 17.8% higher than the k-shortest method, 306.2% higher than AMPLE, and 164.2% higher than the single-path method. Figure 6: Comparison of average packet loss rate among different methods with the increasing number of flows: (**a**) when the device moves to S10; (**b**) when the device moves to S12. This is because the RANK method maximizes and balances the transmission capacity to each destination node. A higher average transmission capacity typically leads to higher overall throughput. However, it is important to note that maximizing the average transmission capacity does not necessarily ensure that the transmission capacity from the source node to every individual destination node is also maximized. In Algorithm 2, due to the flow entry constraints of the switches, we must discard certain paths.