# Computation Offloading and Resource Allocation Based on P-DQN in LEO Satellite Edge Networks
## 3 System Model and Problem Description  
### LEO Satellite Edge Network Model  
The LEO satellite edge network model is shown below in Figure 1.  
As shown in Figure 1, the network includes multiple ground terminals, several LEO satellites equipped with edge servers, and one cloud server. Let \(\mathcal{L}=\{1,2,\ldots,L\}\) be the satellite set, with \(L\) as the total number of satellites. Designate that LEO satellites use Ka-band (27-40 GHz) to provide access for ground terminals, and each satellite only takes charge of terminals within its coverage. Moreover, let \(\mathcal{K}=\{1,2,\ldots,K\}\) be the division of \(K\) regions, and then let \(\mathcal{I}_{k}=\{1,2,\ldots,I_{k}\}\) be the set of terminals in region \(k\). Assume that all terminals within one coverage access the same satellite (each terminal, yet, can only access one satellite at one time), while each satellite can serve multiple terminals simultaneously. Since terminals within the same coverage have similar distances, the channel states (between terminals and LEO satellites) are almost identical, and the time division multiple access (TDMA) can work to avoid multi-user interference within the region. Next, let \(M\) be the cloud server. Due to the long distance and sophisticated geographical conditions, a direct connection between \(M\) and terminals cannot be established. Thus, the service flow from terminals must be forwarded through LEO satellites to \(M\).  
To better depict dynamics in the network due to the random arrival of tasks, the system time can be discretized into successive time slots with equal length, i.e., \(\mathcal{T}=\{1,2,\ldots,T\}\). Let \(R_{k,i}^{\dagger}\) be the new arrival task of terminal \(i\) in region \(k\) during time slot \(t\in\mathcal{T}\), and \(l_{k}\in\mathcal{L}\) be the satellite covering region \(k\). Further, all tasks are latency sensitive, and denote \(t_{\max}\) as the maximum tolerance latency per task and \(c_{k,i}^{\dagger}\) as the size per packet to be processed by the task, respectively. Besides, only consider tasks surviving for several time slots, the duration of which is far less than the continuous coverage duration of LEO satellites for one region (which is set as about 9 min in [43]). As such, almost all tasks considered can be terminated (accessed or failed) within the LEO satellite covering the duration, and thus the handover and its associated unstable connections are reasonably ignored. Note that, due to the insufficient computing capability and limited resources in ground terminals, a larger processing latency would be incurred locally. In contrast, when offloading tasks to LEO satellites, a relatively larger propagation latency is preferred.  
Thus, there are three options for the terminal to process task \(R_{k,i}^{\dagger}\), and the latency depends on the computation offloading mode. Let \(\mathcal{X}_{k,i}^{\dagger,t}=\{x_{k,i}^{\dagger,t,1},x_{k,i}^{\dagger,t,2},x_{ k,i}^{\dagger,t,3}\}\) be the offloading set of task \(R_{k,i}^{\dagger}\) at slot \(t\) (originating at \(I\) and not yet completely terminating until \(t\)), where \(x_{k,i}^{\dagger,t,1},x_{k,i}^{\dagger,t,2},x_{k,i}^{\dagger,t,3}\in\{0,1\}\) and \(x_{k,i}^{\dagger,t,1}+x_{k,i}^{\dagger,t,2}+x_{k,i}^{\dagger,t,3}=1\), i.e., each task \(R_{k,i}^{\dagger}\) can only choose one processing method. In particular, \(x_{k,i}^{\dagger,t,1}=1\), \(x_{k,i}^{\dagger,t,2}=1\) and \(x_{k,i}^{\dagger,t,3}=1\) denote that the task is processed locally, offloaded to the satellite, and offload to the cloud server, respectively.