# Satellite Network Task Deployment Method Based on SDN and ICN
## 3 System Model and Problem Formulation
### Task Model
#### 3.4.3 Task Computation Delay  
Because each satellite node can initiate task calculation, multiple subtasks are inevitably deployed in one node. The satellite node evaluates the computation latency of the task by obtaining the local computing task queue. The resources of a single LEO satellite are, however, very limited. Therefore, it is necessary to consider the computing and caching resources that a single satellite can provide when deploying a mission. Here we assume that the onboard processor is a single-core, single-threaded processor. Each satellite has a task queue, and the tasks in the queue have three states: running, ready, and waiting. The ready state indicates that the task has completed collecting the data required by the task and is waiting to obtain the CPU usage. The waiting state indicates that the computing task has been deployed to the node, but the data required by the task has not been collected, or the precursor task has not been completed, waiting for the output and completion signal of the precursor task. When the task completes data collection, it switches to the ready state. If \(F_{m}\) is the clock frequency of the LEO satellite and \(f_{m}\) is the clock frequency assigned to the subtask, the delay required to complete the subtask \(task_{i}(C_{i},R_{i},G)\) is:  
\[t_{l}=\frac{R_{i}}{f_{m}},f_{m}\leq F_{m} \tag{9}\]  
The data capacity required by the subtask should also be less than the capacity that the satellite node can provide. \[R_{n}\leq v_{m},\forall m\in M \tag{10}\]The task computation delay includes the waiting delay in the queue and the computation-required delay. The waiting time is the time for the satellite node to complete the task of the current calculation queue. The waiting delay \(t_{w}\) is calculated by the satellite node and uploaded to the SDN control node. Therefore, the time delay is:  
\[Z_{n}^{3}=t_{w}+t_{l} \tag{11}\]  
The delay of task processing includes the delay of task deployment, the delay of data transmission, and the delay of task computation. The total deployment delay of the task is:  
\[Z_{n}=Z_{n}^{1}+Z_{n}^{2}+Z_{n}^{3}=\max\{t_{b1},t_{b2}\ldots t_{bm}\}+\max\{T_ {o_{1}},T_{o_{2}}\ldots T_{o_{n}}\}+t_{w}+t_{l} \tag{12}\]  
Deploying edge computing on the LEO satellite network improves the response time of terminal computing tasks and reduces the amount of traffic back to the ground-based cloud computing center. However, the communication burden of the LEO satellite network is increased due to the mission deployment and the data transmission required by the mission. Note that task processing needs to also consider QoE. Therefore, this paper combines the communication volume and task response delay caused by edge calculation to develop the joint objective function:  
\[Q_{n}=\alpha Z_{n}+\beta F_{n} \tag{13}\]  
where \(\alpha,\beta\in[0,1]\) and \(\alpha+\beta=1\). \(\alpha\) and \(\beta\) are the balanced relationship between task processing delay and task traffic. For delay-sensitive tasks with large computation and small communication volume, \(\alpha\) and \(\beta\) should be increased and decreased, respectively. For tasks with large communication volume, such as video service, which are less sensitive to time delay, \(\beta\) should be increased and \(\alpha\) decreased. Therefore, these parameters should be set dynamically during task deployment according to task requirements. According to the above modeling, SDN-based satellite network task deployment involves resource allocation amongst multiple satellites, and there are many ways to deploy a single task. If the number of task deployment nodes is \(M\) and the number of tasks is \(N\), the time complexity is \(O(M^{N})\); hence, it is a complex combinatorial optimization problem. Therefore, the optimization goal in this paper is an NP-complete problem--that is, the time complexity in the worst case increases exponentially with the scale of the problem. Therefore, the task deployment strategy cannot find the optimal solution in polynomial time complexity.