# Scheduling Sparse LEO Satellite Transmissions for Remote Water Level Monitoring
## 3 Findings
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Preference Model** & **Success Prob. \(p_{success}\)** & **Attempt Rate \(r_{attempt}\)** & **Average Power** & **Required Battery Capacity** \\ \hline \multirow{3}{*}{1} & 0.13 & 2.564 h\({}^{-1}\) & 67.54 mW & 592.1 Wh \\  & 0.13 & \(\frac{1}{24}\) h\({}^{-1}\) & 3.810 mW & 33.40 Wh \\  & 0.20 & \(\frac{1}{24}\) h\({}^{-1}\) & 3.735 mW & 32.74 Wh \\ \hline \multirow{3}{*}{2} & 0.42 & 0.7937 h\({}^{-1}\) & 29.31 mW & 256.9 Wh \\  & 0.42 & \(\frac{1}{27}\) h\({}^{-1}\) & 3.575 mW & 31.34 Wh \\  & 0.57 & \(\frac{1}{25}\) h\({}^{-1}\) & 3.405 mW & 29.85 Wh \\ \hline \multirow{3}{*}{3} & 0.78 & 0.4274 h\({}^{-1}\) & 14.95 mW & 131.1 Wh \\  & 0.78 & \(\frac{1}{27}\) h\({}^{-1}\) & 3.234 mW & 28.35 Wh \\  & 0.85 & \(\frac{1}{27}\) h\({}^{-1}\) & 3.151 mW & 27.62 Wh \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Sample energy savings from simulated packet scheduling for a year of operation For simulated baseline values, the average time to attempt is represented as the first available satellite pass, expressed by  
\[t_{SL,baseline}=\frac{p_{success}}{r_{pkt}}\Rightarrow r_{attempt,baseline}=\frac{r_{ pkt}}{p_{success}},\]  
which represents the algorithm for determining \(t_{min}\), where successful transmission lead to waiting a minimum of \(\frac{1}{r_{pkt}}\) hours, while unsuccessful attempts lead to no minimum wait. The results demonstrate that online learning direct-to-satellite packet scheduling is capable of reducing average power and battery requirements around 20 times. Note that the dominant energy saving comes from reducing average attempt frequency, although the improved success rate of the scheduling algorithm introduce significant power saving. Additionally, our direct-to-satellite packet scheduling scheme enabled us to lower the attempt frequency, as it provides a built-in mechanism for selecting future passes. Tradeoff between Low Power and Learning Rate  
The proposed algorithm in its current state exhibits low average attempt rate values \(r_{attempt}\) (still sufficiently high for the intended application). The discount factor parameter \(\lambda\) is investigated in Figures 14-16, as it impacts the transmission attempt rate and thus the time a node takes to learn, as well as the time to transmit and the modem power. Figures 14 and 15 show that with low values of \(\lambda\), future candidate passes are all discounted to such a degree that the resultant probabilities from the softmax function show little to no preference for earlier passes. Furthermore, with high values of \(\lambda\) (very close to 1), we observe that future candidate passes are all so little discounted that the resultant probabilities from the softmax function show little to no preference for earlier passes. It is only for \(\lambda\) values from around 0.9 to 0.95 (\"sweet spot\") that the values of future candidate passes are discounted such that there is an apparent preference for earlier passes, such that the transmission success and time to transmit are more favorable. Figure 14: Average success rate versus discount factor \(\lambda\) for bucketed noise and moderate preference model 2. Earlier passes means more frequent transmission attempts. A downside to this is in smaller expected power savings, as more frequent transmissions require significantly more average power. There is thus a tradeoff between having a high learning rate and achieving low average power consumption, Figures 14-16, with the \"sweet spot\" area of \(\lambda\) selected for all earlier experiments, e.g., Table 9.