## 4 Proposed Routing Scheme
### Distributed Detour Routing Scheme
Similarly, if a link failure occurs in the upward or downward direction, the MHR is extended in the opposite directions. In the extended MHR, the returned packet undergoes the same procedure as a detour packet. That is, the node that receives the returned packet forwards it through a detour path. Because the source node has already received the link failure information from the returned node, selective flooding is unnecessary. In case the extended MHR is in the seam or polar region, extending the MHR in the direction opposite to the primary direction can lead to packet drop. If the MHR extends into the seam or polar region, the MHR extends in the direction opposite to the secondary direction of the detour. When the MHR extension reaches the seam, the cross-seam ISL remains unconnected. Extending in the direction opposite to the primary direction may not be feasible. When the direction opposite to the primary cannot be connected, the opposite direction of the secondary direction is selected for the detour. If both the primary and secondary direction extensions are impossible, then all four links are unavailable. In all three cases, the direction of the returned packet is determined by the rapid detour direction. Additionally, because the returned packet contains information on the failed link, there is no need for additional selective flooding. ## 5 Performance Evaluation

In this section, the performance of the distributed detour routing scheme is presented. The main performance metrics for link failure include end-to-end delay and communication overhead. Furthermore, the extra delay and number of hops for the detoured packet path are investigated using the detour algorithm. Finally, the ISL utilization of the detour path is examined with regard to unstable links. ### Simulation Setup

The simulations were conducted on an Iridium-like LEO satellite network to evaluate the performance of the proposed distributed detour routing scheme. The Iridium satellite network comprises 66 satellites with six orbits [1]. That is, each orbit has 11 satellites. Each satellite has four ISLs: two intra-ISLs and two inter-ISLs. The LEO satellites in the polar and seam regions have three ISLs and two ISLs, respectively. The LEO satellite altitude was 780 km and its inclination was 86.4\({}^{\circ}\). Similar to related studies on LEO satellite networks [7], we set the polar boundary of each hemisphere to 70\({}^{\circ}\). We transmitted each packet at a constant rate. We assumed the ISL rate was set to 100 Mbps. This conservative value is achievable with current laser communication terminals [9]. Packets were randomly generated across the entire network topology following a uniform distribution and were transmitted by selecting paths according to hop-by-hop routing. The simulation parameters are listed in Table 1.

In our satellite network, the number of failed ISLs was determined by the link failure rate and was randomly selected from 222 ISLs. Link failure rates follow a uniform distribution in accordance with a uniform traffic distribution. Subsequently, these ISLs were \begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameter** & **Value** \\ \hline The number of orbits & 6 \\ The number of satellites per orbit & 11 \\ Altitude & 780 km \\ Inclination & 89\({}^{\circ}\) \\ ISL interface per satellites & 4 \\ Packet size & 1 KB \\ Polar-boundary & 70\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of the simulation. designed to fail at random times within the simulation time. When using a laser module for ISL, the link setup time ranged from a few seconds to tens of seconds [25]. Therefore, link recovery was ensured to occur within a maximum of one minute after the beginning of link failure. The performance of the proposed distributed detour routing scheme was compared with those of two benchmark schemes. The detailed benchmark schemes are as follows:

* Orbit prediction shortest path first (OPSPF) [7]: In this scheme, the periodic exchange of hello messages was used to detect link failure.