# AoI Analysis of Satellite-UAV Synergy Real-Time Remote Sensing System
## 2 System Model
### Queuing Disciplines  
To facilitate the study of AoI, the status information update systems are typically modeled as queuing systems, where arriving status information is served following queuing disciplines [43]. In this paper, the AoI\({}_{0}\) performance is analyzed under three queuing disciplines that are commonly considered in research.  
Define tuple \(\mathbf{a}=(a_{1},a_{2})\), where \(a_{1}\) denotes the number of \(m_{1}\) currently being stored in \(queue_{1}\), and \(a_{2}\) denotes the number of \(m_{2}\) stored in \(queue_{2}\). In the following, the three adopted queuing disciplines are described:  
_LCFS_ with no preemption (_LCFS-NP_): Under the _LCFS-NP_ queuing discipline, \(queue_{i}\) has only one storage position and is non-preemptive. In this paper, for a new arriving \(m_{1}\), if \(\mathbf{a}=(0,0)\), the new \(m_{1}\) enters \(queue_{1}\) and GU \(k\) keeps idle. If \(\mathbf{a}=(0,1)\), the new \(m_{1}\) enters \(queue_{1}\) and GU \(k\) starts to generate \(q_{0}\) immediately. If \(\mathbf{a}=(1,0)\) or \(\mathbf{a}=(1,1)\), the new \(m_{1}\) is discarded. For a new arriving \(m_{2}\), it is similar to the above.  
_LCFS_ with preemption in service (_LCFS-PS_): Under the _LCFS-PS_ queuing discipline, \(queue_{i}\) has only one storage position and is preemptive. The new arriving packets are allowed to preempt packets in service and packets in waiting. In this paper, for a new arriving \(m_{1}\), if \(\mathbf{a}=(0,0)\), or \(\mathbf{a}=(0,1)\), the management of the packet under _LCFS-PS_ is same as the _LCFS-NP_ one. If \(\mathbf{a}=(1,0)\), the new \(m_{1}\) preempts the old one stored in \(queue_{1}\), and the old one is discarded, GU \(k\) keeps idle. If \(\mathbf{a}=(1,1)\) (i.e., GU \(k\) is generating \(m_{0}\)), the new \(m_{1}\) preempts the old one stored in \(queue_{1}\), and the old one is discarded. GU \(k\) restarts to generate \(m_{0}\) based on the new \(m_{1}\) and the \(m_{2}\) stored in \(queue_{2}\). For a new arriving \(m_{2}\), it is similar to the above.  
_LCFS_ with preemption in waiting (_LCFS-PW_): Under the _LCFS-PW_ queuing discipline, \(queue_{i}\) has two storage positions and is preemptive. The new arriving packets are only allowed to preempt packets in waiting. In this paper, for a new arriving \(m_{1}\), if \(\mathbf{a}=(0,0)\), or \(\mathbf{a}=(0,1)\), or \(\mathbf{a}=(1,0)\), the management of the packet under _LCFS-PW_ is the same as the _LCFS-PS_ one. If \(\mathbf{a}=(1,1)\) or \(\mathbf{a}=(1,2)\), the new \(m_{1}\) enters \(queue_{1}\). If \(\mathbf{a}=(2,1)\) or \(\mathbf{a}=(2,2)\), the new \(m_{1}\) preempts the old one stored in the second position of \(queue_{1}\) and the old one is discarded. For a new arriving \(m_{2}\), it is similar to the above.  
In this section, the physical layer communication of the system is built up in the communication model. The information fusion process and the information transmission process are considered in the AoI analysis model. This establishes the relationship between  
Figure 2: An illustration of the AoI analysis model for the fused information in satellite–UAV “multiscale explanation” synergy remote sensing scenario.  
the AoI of fused information and the communication resources of SAGIN. The management for arriving status information is governed by the queuing disciplines. The closed-form expressions of MGF can be derived based on this model, which provide the theoretical basis for AoI analysis in SAGIN in Section 4.