# A Disruption Tolerant Distributed Routing Algorithm in LEO Satellite Networks
## 4 Detailed Algorithm Description  
### Algorithm Parameters and Performance Analysis  
Since the services carried by the space segment network mainly go through three to four hops, we compared the routing performance of the strategies in which the link failure information is propagated to one hop, two hops, and three hops for the V1 -> V9 data flow in a 3 \(\times\) 3 network topology. As shown in Figure 5, \(latV1=latV3\), \(latV1>latV7\), \(latV7-latV4=latV4-latV1\). The main path of V1 -> V9 is V1-V2-V3-V6-V9, and the failed link is V6-V9. Due to the long intersatellite link length, and the buffer size of the space router being relatively small compared to the laser link bandwidth, the transmission delay of the data packet is much smaller than the propagation delay. We take the propagation delay \(t\) and the detour distance \(d\) as the evaluation index of the detour path, the propagation delay \(t=L/c\), where \(L\) is the total length of the intersatellite link that the detour path passes through, and \(c\) is the speed of light, which is used to measure the quality of service provided by the detour path, while the detour distance \(d\) is represented by the graphic area enclosed by the detour path and the main path, which is used to measure the load balancing capacity of the detour path for the intersatellite link. Let \(L_{h}1\) represent the length of the ISL V1-V2, \(L_{h}2\) represent the length of the ISL V4-V5, \(L_{h}3\) represent the length of the ISL V7-V8, and \(L_{v}\) represent the length of intra-plane ISL. If the link failure information is propagated to one hop, the data flow starts to detour when it reaches V3. The detour path is V1-V2-V3-V2-V5-V8-V9. Under this circumstance, the propagation delay \(t1=(3L_{h}1+L_{h}3+2L_{v})/c\), the detour distance \(d1=2\). When the link failure information is propagated to two hops, the data flow starts to detour when it reaches V2, and the detour path is V1-V2-V5-V8-V9. In this case, the propagation delay \(t2=(L_{h}1+L_{h}3+2L_{v})/c\), the detour distance \(d2=2\). When the link failure information is propagated to three hops, the data flow starts to detour at V1, and the detour path is V1-V4-V7-V8-V9. In this case, the propagation delay \(t3=(2L_{h}3+2L_{v})/c\), the detour distance \(d3=4\). The above only exemplifies the failure of V6-V9, and V1-V2, V2-V3, and V3-V6 will also fail with the same probability. Under the premise that each link in the network fails with equal probability, the routing performance under various strategies is comprehensively analyzed, and the calculation results are as follows:  
1. Dissemination of failure information to one hop. \(t1=(4L_{h}1+5L_{h}2+L_{h}3+8L_{v})/4c\), \(d1=1.75\). 2. Dissemination of failure information to two hops. \(t2=(L_{h}1+6L_{h}2+L_{h}3+8L_{v})/4c\), \(d2=2\). 3. Dissemination of failure information to three hops. \(t3=(6L_{h}2+2L_{h}3+8L_{v})/4c\), \(d3=2.5\). The strategy of dissemination of failure information to one hop is obviously undesirable because of repetitive paths and poor diversion capabilities. We compare the strategies of dissemination of failure information to two hops and three hops. Derived from the Section 2,  
\[L_{h}=\sqrt{2}R\sqrt{1-\cos(\varphi)+(1-\cos(RI))\cos(latA)\cos(latB)}. \tag{6}\]  
Figure 5: Comparison of strategies for different synchronization hops. The variables in this formula are \(latA\) and \(latB\), in \(L_{h}1\), \(latA=latV1\), \(latB=latV2\), in \(L_{h}3\), \(latA=latV7\), \(latB=latV8\), since \(latV1>latV7\), \(latV2>latV8\), so \(L_{h}3>L_{h}1\), \(t3>t2\). According to the changing law of the cosine function, when the satellite is at low latitudes, the change of \(L_{h}\) is relatively gentle, but at high latitudes, the change is relatively large, so that the strategy of dissemination of failure information to two hops has an obvious advantage on delay at high latitudes.