# Research on Task-Oriented Computation Offloading Decision in Space-Air-Ground Integrated Network
## 2 Materials and Methods
### Computation Offloading Decision Process  
In this section, combining with Markov Decision Process Principle, the tasks are offloaded to the ground-based backbone nodes, the edge access nodes, or the space-based backbone nodes according to their own locations and requirements. Figure 2 shows the model of the computation offloading decision process based on Markov Decision. The offloading terminals (offloader) of the Space-Air-Ground Integrated Network are the terminal devices at various positions in the network, and the offloading sites (offloadede) are offloaded sets that can provide a variety of computing nodes choices for tasks. The terminal devices in the network are in high-speed movement states. When processing high-intensity tasks, the signal strength of the wireless network coverage of the offloading sites will be weakened due to the prolonged processing time. Therefore, the huge and complex task is divided into several independent subtasks using the divide and conquer thinking, and the continuous task processing process is abstracted into the state transition process of the Markov model to reduce the series of effects caused by the dynamic change of the position of the terminal devices. Taking the offloading tasks (offloader tasks) in the edge access network as an example, the entire Markov decision process is constructed. Define \(V_{in}\) as the \(i\)-th task of the current terminal device \(n\). The location of the offloading terminals and the offloading execution terminals are not fixed. During the task offloading execution, the wireless channel performance from the terminals to the servers in the space-based backbone network, the ground-based backbone network, or edge access network is constantly changing. And the higher the transmission delay, the more difficult it is to guarantee the transmission quality of the wireless channel. Therefore, it is necessary to fully consider the factors that affect the network status during the task offloading execution. In the process of task offloading, to minimize the delay and  
Figure 2: Markov State Transition Model. The Space–Air–Ground Integrated Network is abstracted into an offloading network model represented by Markov states, with \(i\) denoting the task offloading location and circles de-noting the Markov states in each decision period. Taking the edge access network in the middle layer as an example, the whole Markovian decision process is given, which is represented by gray circles. energy consumption of task computation offloading, it is necessary to keep the current task offloading network as the most optimal network. When the terminal devices leave the scope of the offloading network which is currently executed by the offloading task, or a new offloading network that meets the offloading conditions is added, the original offloading network will change. At this time, switching through the network should be considered to complete the task offloading. Figure 3 shows the flow chart of network switching in the process of task computation offloading of the Space-Air-Ground Integrated Network. Figure 3: Network Switching Flowchart. This figure represents the network selection and switching process during task offloading. Network switching is always present during the whole task offloading process, always keeping the network where the current task is offloaded as the optimal network, so that the delay and energy cost of task offloading are minimized. When the computational resources of the offloading sites do not meet the offloading conditions, it's essential to select new offloading sites or perform network switching or abandon the task computation offloading and change to execute at local terminal devices. However, due to the complex environment of the Space-Air-Ground Integrated Network, the offloading network is prone to network interruption during the switching process.