# A Computation Offloading Strategy in LEO Constellation Edge Cloud Network
## 5 Numerical Simulation
### Simulation Results  
Figure 8 depicts the satellite resource max utilization under three different offloading strategies with different constellation sizes. From the simulation results, we can find that the utilization of satellite computing resources is only about 20% using the access satellite offloading strategy, and no more than 50% using the neighbor offloading strategy, and the joint optimization offloading strategy can make full use of the satellite computing resources of the whole system to improve the utilization efficiency of the constellation edge cloud network system. For example, constellation 2 with 72 satellites, as shown in Figure 9, under access satellite offloading strategy, the satellite resource utilization with each concurrent tasks demand varies slightly in fluctuations. As the number of offloading tasks increases, the whole constellation satellite resource utilization is maintained at no more than 20%. The neighbor satellite offloading strategy utilizes the neighbor node of the satellite directly connected to the satellite terminal, which has a higher resource utilization ratio than the access satellite strategy, but it does not increase after exceeding the computing capacity of all the neighboring satellites. In practice, the more imbalanced distribution of tasks will lead to lower utilization of satellite resources. Figure 10 shows the task response rate under the constellation 3 of 144 satellites with different concurrent tasks. It can be seen that as the number of tasks increases, the task response rate decreases gradually under the offloading strategy of access satellites and neighbor satellites, and the all-constellation joint offloading strategy can meet the access of more offloading tasks. In the scenario of whole-constellation offloading, it can be seen from Figure 11 that the satellite resources utilization rate under the joint optimization strategy is the highest, which is 40% higher than the random offloading strategy and about 20% higher than the FirstFit strategy. When the computational capacity of the whole constellation meets the requirements of all offloading tasks, the joint optimization strategy can maintain the task response rate of 100%, while the random strategy and FirstFit strategy both begin to decline when the number of concurrent tasks reaches a certain value, as shown in Figure 12. In constellation 2 with 72 satellite scenarios, Figure 13 shows the three offloading strategies of energy cost. It is obvious that the joint optimization offloading strategy has the lowest energy costs, and the first fit strategy only considered the calculation of energy cost, and ignored the optimal choice of the path, causing the total energy cost at the highest levels. Figure 14 shows the load balancing costs of the three offloading strategies under 72 satellites. The joint optimization strategy has the lowest load cost because the load balancing level is an important optimization item in the joint optimization. The first fit strategy greedily selects the satellite node with the most remaining resources each time, which also has a certain load balancing effect. The random strategy does not consider the load between satellite resources, and the load balancing cost is the highest. From the simulation results of Figure 15, we know that the joint cost of the joint optimization strategy is the lowestin the three whole constellation offloading strategies, and the joint cost of the random strategy is higher than the first fit strategy. This is because the weight coefficient \(\beta\) of the objective function is set to 5, which causes load balancing to affect their joint cost. However, no matter how \(\beta\) changes, the cost of the joint optimization strategy will remain the lowest.