QPS/(TCO×CO₂) Efficiency Metric

• QPS/(TCO×CO₂) metric is a composite measure that jointly assesses system throughput, total cost of ownership, and carbon emissions.
• It aggregates performance data, cost models, and emission estimates to enable rigorous lifecycle evaluation of computing systems.
• The metric guides upgrade planning and policy decisions to improve data center efficiency and promote sustainable operational practices.

The QPS/(TCO×CO₂) metric is a composite efficiency measure used to assess compute infrastructure by jointly evaluating its throughput (QPS: queries per second), total cost of ownership (TCO), and carbon emissions (CO₂). This metric has emerged in response to the need for holistic performance indicators that balance computational capability with financial and environmental costs, particularly in large-scale data center operations and sustainable engineering contexts. By encapsulating performance, economic investment, and climate impact, QPS/(TCO×CO₂) enables rigorous comparison and optimization across different system architectures, deployment strategies, and lifecycle management approaches.

1. Formal Definition and Interpretation

The formal definition provided in the literature (Nikolaou et al., 7 Oct 2025) is: $\text{Efficiency} = \frac{\text{QPS}_{\text{agg}}}{\text{TCO}_{\text{total}} \times \text{CO}_2_{\text{total}}}$ where:

• $\text{QPS}_{\text{agg}}$ : aggregate number of queries completed by the system over its lifetime,
• $\text{TCO}_{\text{total}}$ : cumulative capital (CAPEX) and operational (OPEX) costs,
• $\text{CO}_2_{\text{total}}$ : total carbon emissions, including both embodied and operational components.

This formulation is used to rank or optimize system configurations, with higher values corresponding to better joint performance–cost–emissions trade-offs. In practice, all terms are computed over the system's full depreciation period.

2. Components and Calculation Methods

Queries-per-Second (QPS)

QPS quantifies system throughput. In data centers, this is typically measured using benchmarking suites such as SPECpower, generating normalized QPS scores for hardware units. Aggregation accounts for the time-weighted contribution of each server: $$\text{QPS}_{\text{agg}} = \frac{\sum_{i=1}^{N} QPS_i \cdot (d_i \times \text{seconds})}{L}$$ where $d_i$ is the duration each server is in use, $QPS_i$ is its throughput, and $L$ is the total operational lifetime.

Total Cost of Ownership (TCO)

TCO sums all system expenditures: $TCO = CAPEX + OPEX$ with

• $CAPEX$ including server hardware (CPU, DIMM, etc.) costs,
• $OPEX$ derived from active power consumption:

$$OPEX = \text{Server}_\text{Power} \times d \times \text{KiloHours/year} \times \text{energy\_cost}$$

CAPEX and OPEX are aggregated for all servers over their respective usage periods.

Carbon Dioxide Emissions (CO₂)

CO₂ quantification uses models such as ACT, combining embodied emissions (from manufacture) and operational emissions (energy use). The total CO₂ may be computed per server and then summed across the system lifetime.

3. Optimization via Upgrade Planning

The QPS/(TCO×CO₂) metric is sensitive to upgrade scheduling. The referenced paper (Nikolaou et al., 7 Oct 2025) explores two approaches:

• Global Upgrade Plan: Formulated at design time using foresight into future server models. It allows variable-length upgrade cycles and selection from future hardware releases.
• Local Upgrade Plan: Employs a fixed, equal-length upgrade cycle with selection limited to currently available models.

Global planning over the full lifecycle maximizes the QPS/(TCO×CO₂) metric. The paper found a 19% improvement with global plans relative to the best local alternative, highlighting the benefit of forward-looking scheduling.

Upgrade Decision Factors

Optimization considers:

• Server entry year,
• Performance benchmarks,
• Active power profiles,
• Capital costs,
• CO₂ profiles.

Each timeline partition (server use period) is exhaustively analyzed for its aggregate impact on the three metric dimensions.

4. Cross-Domain Applications and Extensions

Though developed for data center upgrade strategy, similar composite metrics have arisen in scientific computing and power grid optimization domains.

• EcoL2 (Kapoor et al., 18 May 2025) provides an alternative bounded metric for neural PDE solvers, balancing relative error and multi-stage lifecycle carbon emissions. While QPS/(TCO×CO₂) aggregates query throughput, cost, and emissions, EcoL2 uses tunable parameters ($\alpha$, $\beta$) to weight accuracy against carbon cost for model selection and deployment.
• Power grid optimization (Cho et al., 17 Jun 2025) employs CO₂-enhanced cost functions, enabling analogs of QPS/(TCO×CO₂) for evaluating operational performance against combined economic and carbon criteria. Generator-level emissions, fuel-type categorization, and carbon-aware optimal power flow (OPF) objectives provide a direct framework for metric calculation.

5. Flexibility, Time-Dependency, and Policy Implications

Metric effectiveness is pathway-dependent. As shown in GHG policy analysis (Tanaka et al., 2020), the cost-effective translation of non-CO₂ emissions is highly sensitive to mitigation pathway and timing. A static metric across time and scenarios induces suboptimal mitigation costs; flexible, periodically reappraised conversion factors (akin to GCP in climate economics) are needed.

This suggests that QPS/(TCO×CO₂) should be designed as a time-adaptive metric: recalibrated as technology, energy sources, and emissions profiles evolve. Integrated assessment and benchmarking frameworks benefit from incorporating scenario-dependent weighting of cost and carbon terms.

6. Practical Impact and Future Directions

The QPS/(TCO×CO₂) metric is moving from theoretical construct to practical adoption in data center management, sustainable computing, and grid operations. Its use facilitates:

• Lifecycle planning that explicitly accounts for environmental constraints.
• Hardware selection and upgrade schedules that maximize efficient throughput per cost and emissions.
• Policy development and compliance, particularly as carbon costs become internalized in operational economics.

Challenges remain. Accurate prediction of future hardware specifications is required for global planning; scalable solvers must address the combinatorial complexity as model space expands. As energy markets, carbon pricing, and technology trajectories become more uncertain, probabilistic models and scenario analysis may supplement exhaustive deterministic strategies.

A plausible implication is the integration of such composite metrics into real-time monitoring dashboards and procurement pipelines, guiding operational decisions toward joint economic and environmental long-term optima. The approach helps forge clearer connections between the technical, fiscal, and sustainability agendas that increasingly shape critical infrastructure.