# A Computation Offloading Strategy in LEO Constellation Edge Cloud Network
## 3 System Model
### Communication Model  
We assume that each satellite terminal uses TDMA multiple access and can access only one satellite at a time. Benefiting from the global coverage of low-orbit constellations, satellite terminals can always be covered by low-orbit satellites. The satellite-ground link  
\begin{table}
\begin{tabular}{c l} \hline \hline \(\mathcal{M}\) & Set of LEO satellite \(m\) \\ \(\mathcal{N}\) & Set of ground terminals \\ \(\mathcal{W}\) & Set of computation task \\ \(D_{n}\) & Data size of task \(n\) \\ \(C_{n}\) & Number of CPU cycles for task \(n\) \\ \(B_{n}\) & Channel bandwidth of ground terminal \(n\) \\ \(G_{t}\) & Transmitting antenna gain of ground terminal \(n\) \\ \(G_{r}\) & Receiving antenna gain of ground terminal \(n\) \\ \(L_{p}^{\mathrm{gs}}\) & Rain attenuation of ground-satellite link \\ \(L_{n}^{\mathrm{gs}}\) & Free space loss of ground terminal \(n\) \\ \(Ng^{\mathrm{gs}}\) & Noise power of ground terminal to access satellite \\ \(p_{n}^{\mathrm{gs}}\) & Transmit power of ground terminal \(n\) \\ \(R_{ij}^{\mathrm{ss}}\) & Inter-satellite link transmit rate from satellite \(i\) to \(j\) \\ \(K_{b}\) & [PERSON]’s constraint \\ \(T_{s}\) & System noise temperature \\ \(E_{b}/N_{0}\) & Ratio of received energy-per-bit to noise power density \\ \(P_{ij}^{\mathrm{gs}}\) & Transmit power of satellite \(i\) to satellite \(j\) \\ \(L_{i,j}^{\mathrm{ss}}\) & Free space loss of the inter-satellite link \\ \(G(k)\) & Graph of the \(k\) topology snapshots \\ \(V\) & Set of satellite nodes in the graph \(G(k)\) \\ \(E(k)\) & Set of inter-satellite links in the \(k\) snapshot \\ \(F_{m}\) & Maximum CPU cycles provided by onboard MEC server \\ \(E_{n,m}^{p}\) & Energy consumed on the path from ground terminal \(n\) to service satellite \(m\) \\ \(E_{n,m}^{p}\) & Energy that service satellite \(n\) consumes for task \(n\) \\ \(hop\) & Number of hops ground terminal to service satellite \\ \(f_{m}\) & CPU frequency of the MEC server on the satellite \(m\) \\ \(\Theta\) & The total cost of compute and path \\ \hline \hline \end{tabular}
\end{table}
Table 2: Notation definitions.  
Figure 3: Compute offloading process.  
and the inter-satellite link use microwaves. Satellite terminals uplink transmit rate \(R_{n}^{gs}\) can be expressed as [10]:  
\[R_{n}^{gs}=B_{n}\log_{2}\left(1+\frac{P_{n}^{gs}G_{r}G_{t}L_{p}^{gs}L_{n}^{gs}}{N ^{gs}}\right),\forall n\in\mathcal{N} \tag{1}\]  
where \(B_{n}\) denotes the channel bandwidth of satellite terminal \(n\). \(G_{t}\) and \(G_{r}\) stand for the transmitting antenna gain and the receiving antenna gain, respectively. \(L_{p}^{gs}\) denotes the rain attenuation. \(L_{n}^{gs}\) is the free space loss. \(N^{gs}\) denotes the noise power from ground to access satellite. \(P_{n}^{gs}\) denotes transmit power of satellite terminal \(n\). The inter-satellite link transmit rate \(R_{i,j}^{ss}\) is computed as [11]  
\[R_{i,j}^{gs}=\frac{P_{i,j}^{gs}G_{r}G_{t}L_{i,j}^{ss}}{K_{b}T_{s}(E_{b}/N_{0})},\forall i,j\in\mathcal{M} \tag{2}\]  
where \(K_{b}\) is Boltzmann's constant, \(T_{s}\) is the system noise temperature, and \((E_{b}/N_{0})\) is the ratio of received energy-per-bit to noise power density. \(P_{i,j}^{ss}\) denotes the transmit power of satellite \(i\) when data are sent to satellite \(j\). \(L_{i,j}^{ss}\) is the free space loss of the inter-satellite link. We assume the transmitted power \(P_{n}^{gs}\) and \(P_{i,j}^{ss}\) are fixed values, and thus the energy consumption is proportional to the time transmitting data from satellite terminal to satellite.