Power Modeling Methodology

• Power Modeling Methodology is a data-driven framework that uses hardware performance counters to model and estimate energy consumption in subsystems.
• It leverages automated counter selection and linear regression to achieve fast, accurate power monitoring with minimal overhead.
• Its in-kernel integration, exemplified by the Runmeter framework, enables dynamic power management and workload-aware DVFS for heterogeneous systems.

Power modeling methodology encompasses the systematic strategies, mathematical frameworks, and practical tools used to estimate, monitor, and manage the power consumption of complex computing systems. In contemporary embedded and heterogeneous environments, accurately modeling power is critical for energy-aware design, dynamic power management (DPM), workload-aware DVFS (Dynamic Voltage and Frequency Scaling), and real-time scheduling. The methodology described in "Data-Driven Power Modeling and Monitoring via Hardware Performance Counter Tracking" (2506.23672) represents an archetype of modern, automated, and low-overhead power modeling suitable for integration within operating system kernels.

1. Conceptual Foundation and Model Structure

The methodology implements a systematic, data-driven approach in which each hardware subsystem—such as CPU, GPU, or accelerator—is modeled individually at each relevant DVFS state using hardware performance monitoring counters (PMCs) as proxies for internal activity.

For each subsystem $d$ and DVFS state $f_d$, a linear regression model is derived:

$$P_{d}(X_{d, f_{d}}, W_{d, f_{d}}) = L_d + \sum_{i=1}^{N_i} \left( \frac{1}{T} \cdot x_i \right) w_i$$

where:

• $L_d$: constant base (leakage) power,
• $x_i$: event count from PMC $i$ within sampling period $T$,
• $w_i$: regression coefficient for event $i$.

A lookup table (LUT) is built, containing all per-subsystem, per-frequency linear models:

$LUT[d, f_d] = P_{d}(X_{d, f_{d}}, W_{d, f_{d}})$

The system-wide power is calculated as:

$$P_{\text{tot}} = \sum_{d\in D^*} P_{d}(X_{d, f_d}, W_{d, f_d})$$

This compositional modeling enables accurate power estimation at both subsystem and aggregate levels.

2. Automated PMC Selection and Model Training

A central innovation is the automated identification of predictive PMCs for each subsystem and DVFS state, removing the need for a priori architectural expertise.

The process includes:

1. Profiling: Run diverse benchmarks, simultaneously logging all PMCs and on-board power measurements for each $d, f_d$.
2. Normalization: Convert raw event counts into rates (per unit time).
3. Correlation analysis: For every PMC, compute the Pearson correlation coefficient (PCC) with power and retain events passing a significance threshold (p-value ≤ 0.05).
4. Subset selection & PMU constraints: Rank PMCs by their correlation, then select a subset that both maximizes regression accuracy and satisfies hardware PMU limits (e.g., maximum trackable PMCs, incompatibility).
5. Model fitting: Train the model for $d, f_d$ using non-negative least squares (NNLS), which enforces interpretability.

This selection is architecture-agnostic and fully automatable, adapting to hardware with little human intervention.

3. Runmeter: In-Kernel Power Monitoring and Model Execution

The methodology integrates power modeling within the Linux kernel via the Runmeter framework. Its principal elements are:

• Sampling and data collection: Hooks placed at every context switch and on periodic scheduler ticks collect live PMC data per core.
• Moving-window accumulation: Synthetic samples are constructed by aggregating raw PMC samples over a configurable window, balancing responsiveness and noise reduction.
• In-kernel evaluation: At each window update, Runmeter evaluates the correct LUT-based model for current DVFS state, using the counters from each subsystem.

A representative formula for multi-core CPU power estimation:

$$P_{\text{CPU}} = L_{\text{CPU}} + \frac{1}{T'} \sum_{i=1}^{\#\text{cores}} \sum_{j=1}^{N_{\text{CPU}}} x_{ij} w_{ij}$$

with $x_{ij}$ as the count for PMC $j$ on core $i$ and $T'$ as the window length.

All computations are executed in fixed-point arithmetic, ensuring negligible additional overhead.

4. Accuracy, Overhead, and Runtime Behavior

Empirical evaluation demonstrates:

• Accuracy: The combined model estimates instantaneous total system power with an average Mean Absolute Percentage Error (MAPE) of 7.5% (for typical frequencies) and average energy error of 1.3%. Subsystem (CPU, GPU) errors are typically lower.
• Responsiveness: By leveraging PMCs—which provide immediate activity feedback—model estimates quickly reflect workload phase changes, unlike analog sensors that exhibit inertia.
• Overhead: Maximum observed kernel overhead is 0.7% CPU time at high context switching rates and low frequencies; overhead decreases with higher operational frequencies and in idle states. Fixed-point implementation further ensures efficiency.
• Robustness: The model tracks non-steady-state power events (e.g., phase transitions, short bursts) more promptly than traditional sensor-based approaches due to the digital nature of PMC data.

5. Applications and Implications for System Management

The decomposable, accurate, and automatable nature of the methodology supports a wide spectrum of real-world applications:

• Workload-aware DVFS: Fine-grained, responsive power estimation enables the operating system or runtime to adjust voltage/frequency settings according to actual load, with direct feedback from each subsystem.
• Closed-loop, power-aware scheduling: With real-time power visibility at the sub-task or process level, OS schedulers can optimize task mapping for energy efficiency, thermal constraints, or workload balancing.
• Dynamic Power Management (DPM): Immediate insight into subsystem-level activity allows informed actuation, such as clock gating or resource consolidation.
• Applicability to heterogeneous platforms: The approach’s architectural independence and per-subsystem modeling suit diverse SoCs encompassing CPUs, GPUs, and custom accelerators—without needing detailed microarchitectural documentation.
• Predictive control and future integration: The robust nature of the data stream and low-latency implementation lay the groundwork for advanced predictive or learning-based power management policies within system software.

6. Distinguishing Innovations

Key methodical advancements include:

• Full automation: Reliance on statistically driven PMC selection and model fitting eliminates manual guesswork.
• Sub-system decomposability: Granular modeling at the hardware sub-block level provides high fidelity and adaptability to system heterogeneity.
• Low-overhead, in-kernel realization: The Runmeter implementation illustrates practical deployment at the OS level, overcoming limitations of user-space monitoring or energy estimation.
• Ready integration for energy-centric system design: The methodology is immediately amenable to use in design and deployment phases, with open-source support and minimal platform-specific code modifications.

Summary Table: Methodology Profile

Aspect	Feature/Result
PMC selection	Automated by correlation analysis per subsystem and DVFS state
Model form	Linear (per subsystem/state), LUT-based, non-negative least squares coefficients
Aggregation	System power is sum of subsystem model outputs
Overhead	≤ 0.7% CPU time (worst-case), further reduced at higher frequency/low context switch
Accuracy	≤ 7.5% MAPE power, ≤ 1.3% MAPE energy (full model), subsystem errors lower
Responsiveness	Sub-millisecond, digital; outpaces analog sensors on rapid phase changes
In-kernel integration	Runmeter framework, fixed-point arithmetic
Deployment scope	Heterogeneous, per-subsystem, flexible to platform-specific event sets
Application domain	Real-time scheduling, DPM, workload-aware DVFS, full-stack energy-centric design

Conclusion

This power modeling methodology operationalizes accurate, low-overhead, and responsive energy monitoring for heterogeneous, DVFS-enabled systems by uniting systematic, data-driven PMC selection, linear LUT-based models per subsystem and frequency, and efficient runtime execution in the Linux kernel. The resulting infrastructure is empirically validated to serve as an effective foundation for advanced power-aware operating system policies and workload management in embedded and performance-oriented computing platforms.