## 4 Proposed Routing Scheme
### Distributed Detour Routing Scheme
This is because the proposed scheme prioritizes using the shortest links in the MHR for detouring. As a result, the nodes within the MHR can detour the failed link without relying on it. OPSPF recalculates all routing tables whenever a link failure occurs to ensure an optimal detour path. Therefore, OPSPF is not included in the graph comparing the detour paths. However, DTDR constructs a detour route by prioritizing the secondary direction as an alternative to link failure. The three-hop flooding approach does not know link failure information beyond three hops, and additional routing hops occur in paths exceeding three hops. As Figure 9b shows, there is a one-hop difference in the hop count between the proposed scheme and DTDR. Nevertheless, the proposed scheme selects the ISL with the optimal route within the MHR for detouring. Conversely, the DTDR approach cannot

Figure 8: Average end-to-end delay according to link failure rate. always detour to the optimal point because it uses the \(n\)-hop flooding technique, which introduces additional delays. This means that neither method shows a significant difference in the hop counts of the detour path. However, the proposed scheme generates a shorter detour route for a given hop count. The packet drop rate was further evaluated for the three schemes. Figure 10 shows the packet drop rate according to the link failure rate. The packet drop rate \(PDR\) was calculated as follows:

\[PDR=\text{(Number of packet dropped/Total number of packet sent)}\times 100 \tag{10}\]

OPSPF has the lowest packet drop rate. This is because OPSPF maintains up-to-date network information, ensuring that packets are routed without encountering link failure. However, packets that are transmitted during message flooding do not change their paths because of link-state changes. Consequently, the transmitted packets may encounter link failures and may be dropped. However, DTDR had the highest packet drop rate. This is because packets that encounter a link failure cannot take immediate action and are dropped from the network. The proposed scheme uses rapid detours to route packets that encounter link failure. As a result, it detours the link to reach its destination, which leads to a lower packet drop rate compared to DTDR. If the destination of a packet does not coincide with the intended destination, then the detour table cannot check for link failure information in the path. That means the packet drop rate of the proposed scheme is higher than that of OPSPF. Figure 10: Average packet drop rate according to link failure rate. Figure 9: (**a**) Average end-to-end delay from detour path according to link failure rate; (**b**) average path hop count from detour path according to link failure rate. ### ISL Usage Rate for Flooding Comparison

The ISL laser module requires a PAT process for the link setup with LEO satellites, which results in a significant delay in ISL setup time. In particular, the performance in establishing a link can affect the end-to-end routing delay [27]. An intra-ISL connected within the same orbit can be maintained almost permanently. However, inter-ISL tends to be temporary because of the differences in distance and speed between satellites [25]. In this simulation, to handle unstable links in a more realistic environment, we evaluated the ratio of the ISL used in flooding. Figure 11 shows the ratio between intra-ISL for flooding. In Figure 11, the proposed scheme is only compared with DTDR. A comparison with OPSPF is meaningless because it uses all the network links for flooding. Compared with DTDR, the proposed scheme consistently selects intra-ISL more frequently across all link failures. At a link failure rate of 1%, the proposed scheme uses approximately 10% more intra-ISL than DTDR. This is because the selective flooding path is determined based on the direction and geographical position of the failed link. In particular, link failures occurring in the Northern Hemisphere have selective flooding paths that primarily use intra-ISL.