36 lines
7.1 KiB
Markdown
36 lines
7.1 KiB
Markdown
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## 4. Recommendations
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Our sensitivity and scenario experiments identify a small set of user-controllable levers that dominate battery lifetime. We translate these findings into two layers of recommendations: (i) **what a cellphone user should do first** to maximize time-to-empty (TTE), and (ii) **what an operating system should implement** to automate those gains. The baseline discharge under the reference profile yields a predicted TTE of **4.60 h** with termination by SOC depletion (SOC_ZERO).
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**User recommendations (largest improvements first).** The most effective “everyday” action is reducing display power: halving brightness increases TTE by about **1.22 h** relative to baseline. This aligns with the model’s explicit screen power mapping (P_{\mathrm{scr}}=P_{\mathrm{scr0}}+k_L L^\gamma) and the global sensitivity result that (k_L) has the largest total-effect Sobol index. The second-highest controllable gain comes from reducing sustained compute load (e.g., heavy gaming, prolonged video processing): halving CPU intensity increases TTE by about **0.85 h**. Together, these results imply a simple user rule: *if you can only change one setting, dim the screen; if you can change two, also reduce sustained CPU-heavy usage.*
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**High-risk contexts deserve “protective behaviors,” not incremental tweaks.** Two conditions produce the largest losses and should be treated as “drain emergencies.” First, persistently poor signal reduces TTE from 4.60 h to **2.78 h** (the maximum observed reduction, (-1.82) h). Second, cold ambient conditions reduce TTE to **3.15 h** and switch the termination mechanism from SOC depletion to a premature voltage cutoff (V_{\text{CUTOFF}}), i.e., a user-perceived “sudden shutdown.” Mechanistically, poor signal drives up average power and peak current (radio works harder), while cold primarily increases internal resistance and reduces effective capacity, shrinking voltage margin. Therefore, in weak-signal environments, the best user action is to **prefer Wi-Fi, batch transmissions, or enable airplane mode when offline**, consistent with the non-linear signal penalty (P_{\mathrm{net}}\propto(\Psi+\epsilon)^{-\kappa}). In cold environments, the best action is **warming plus peak-load avoidance** (dim screen, avoid bursts, avoid heavy compute while low SOC) to prevent voltage-limit shutdown.
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**Navigation/GPS is meaningful, but not the sole driver—screen and network often dominate the experience.** Using your 5×4 TTE workload matrix, navigation has longer runtime than gaming at every starting SOC, but still declines steeply with low initial charge—so “start SOC” becomes the practical determinant of whether navigation finishes the trip. This supports a user-facing recommendation: when navigation is necessary and SOC is low, prioritize **screen dimming** and **connectivity management** (map caching on Wi-Fi, reduce background sync), rather than relying on GPS toggles alone.
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| Scenario | 100% Start | 75% Start | 50% Start | 25% Start |
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| -------------- | ---------: | ---------: | ---------: | ---------: |
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| Gaming | 4.11 h | 3.05 h | 2.01 h | 0.97 h |
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| **Navigation** | **5.01 h** | **3.72 h** | **2.45 h** | **1.18 h** |
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| Movie | 6.63 h | 4.92 h | 3.24 h | 1.56 h |
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| Chatting | 10.02 h | 7.43 h | 4.89 h | 2.36 h |
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| Screen Off | 29.45 h | 21.85 h | 14.39 h | 6.95 h |
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From a modeling perspective, GPS enters naturally as an additive term in total power, (P_{\mathrm{tot}}\leftarrow P_{\mathrm{tot}}+P_{\mathrm{gps}}(G)) with (P_{\mathrm{gps}}(G)=P_{\mathrm{gps},0}+k_{\mathrm{gps}}G(t)), making duty-cycling and “accuracy vs battery” tradeoffs straightforward to implement at the OS level.
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**Operating-system strategies: implement a sensitivity-ranked policy stack.** The Sobol results provide a clear prioritization for automated power saving: the dominant drivers are (k_L) (screen), (k_C) (CPU), and (\kappa) (signal penalty). An effective OS should therefore: (1) adopt an aggressive **display governor** that tightens brightness caps as SOC falls; (2) use a **compute governor** that detects sustained high CPU use and shapes it into shorter bursts with idle recovery; and (3) trigger a **“poor signal mode”** under low (\Psi) that reduces scan/transmit aggressiveness and batches network activity, explicitly because the signal penalty is non-linear and thus disproportionately harmful. In cold conditions, the OS should activate a **protective mode** that limits peak current events to avoid voltage cutoff, consistent with the observed shift to (V_{\text{CUTOFF}}) under cold scenarios. Finally, a **navigation mode** should combine (i) dimming, (ii) prefetch/caching over Wi-Fi, and (iii) GPS duty-cycling using (G(t)), since navigation endurance depends strongly on both the screen and connectivity context as well as GPS activity.
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**Aging-aware recommendations: older batteries require earlier peak-power limits.** Our framework models aging through both resistance growth and effective capacity reduction: (R_0(T_b,S)) increases as state-of-health (S) declines, and (Q_{\mathrm{eff}}(T_b,S)) decreases accordingly. This implies that the same workload on an aged battery will reach the voltage limit sooner, especially in cold or weak-signal environments where current demand spikes. Practically, users with older batteries should be advised to avoid “combined stressors” (high brightness + heavy compute + weak signal), and the OS should adapt its low-power thresholds based on estimated SOH—entering protective modes earlier when (S) is low.
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**Generalization to other portable devices is direct under the component-power view.** The same modeling logic extends to tablets, laptops, wearables, and other battery-powered devices by (i) keeping the same electro-thermal state structure and event-based TTE definition, and (ii) replacing the component power decomposition with device-appropriate modules (e.g., larger displays for tablets, CPU/GPU dominance for laptops, and radio/sensor dominance for wearables). The key advantage is that new devices require re-parameterizing component mappings—not redesigning the entire framework.
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**Why we trust these recommendations.** The uncertainty quantification shows that baseline-like usage volatility induces only minute-scale spread in TTE (tight distribution with high survival until near the endpoint), so the hour-scale scenario shifts driving the recommendations remain decisive. Moreover, step-halving verification passes with extremely small relative TTE error across initial SOC levels, supporting that the scenario ranking is not a numerical artifact.
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**Compact priority statement (to close the section):** In short, the highest-return user actions are **dim the screen** and **avoid sustained heavy CPU load**, while the highest-risk contexts are **poor signal** and **cold**, which can even change the shutdown mechanism to voltage cutoff. For OS design, the Sobol ranking implies a policy stack that prioritizes **display control**, then **compute shaping**, then **signal-quality–aware networking**, with an aging/cold protective mode that limits peaks as SOH declines.
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