Execution Time Estimator: Methods & Applications

• Execution Time Estimator (ETE) is a system that predicts software or hardware runtime under fixed conditions using static analysis, profiling, and ML techniques.
• ETE methodologies support real-time scheduling, compiler optimization, and resource provisioning by offering quantitative predictions such as average, worst-case, or full runtime distributions.
• ETE approaches utilize statistical models, regression analysis, and uncertainty quantification to improve accuracy and guide system design and resource allocation.

An Execution Time Estimator (ETE) is any formal, algorithmic, or data-driven system that predicts the runtime or latency of a software or hardware task, before that task is executed, under fixed input and operational conditions. ETEs are essential to real-time systems engineering, scheduling, compiler optimization, resource provisioning, and design-space exploration for modern computing systems. The technical form and granularity of ETEs span static source-code analysis, profiling-based micro-benchmarks, probabilistic models over runtime distributions, ML-augmented simulation, and platform-specific regression models. Their common goal is quantitative prediction—either average, best, worst-case, or full distribution—for execution time on a given platform for a given input, with sufficient accuracy and confidence to aid downstream systems tasks.

1. Methodological Approaches to Execution Time Estimation

ETE architectures cover a range of techniques, each with unique mathematical and practical properties:

• Static Analysis and Profiling: Classical ETEs for logic programs and embedded systems, exemplified by CiaoPP, combine compile-time cost analysis (e.g., resolution/reduction counting) with a one-time empirical profiling step to map abstract cost units to concrete platform-time. After profile calibration, ETE produces upper and lower bounds as closed-form functions of input size and code properties [0701108].
• Measurement-Driven Inference: In the context of worst-case execution time testing for loop-free programs, ETEs employ measurement on a “basis set” of program paths, solve linear/integer programs to infer per-instruction-edge timing, and generate instance-optimal WCET models. This approach yields provable accuracy bounds and quantifies platform timing repeatability (Bundala et al., 2015).
• Program Embedding and Matrix Factorization: In federated computing settings (MPI, cloud), ETEs use observed job logs to create a Programs × Computers matrix; missing execution times are filled by Pearson-correlation–based grouping (“cliques”) or latent-embedding models fit by regularized least squares (ALS). These capture undocumented performance factors without explicit hardware or program features (Chupakhin et al., 2020).
• Probabilistic and Uncertainty Models: ETEs in stochastic scheduling and database query prediction treat execution time as a random variable and fit parametric families (e.g., Exponentiated Weibull, OLL-GG). They explicitly address the “unknown minimum” issue via carefully-designed inference procedures, enabling downstream calculation of P(makespan > deadline) and other risk-aware tasks (Saldanha, 2020, Wu et al., 2014).
• Machine Learning over Structured Features: Recent ETEs leverage extracted code features from source, IR, or binary for early-stage predictions. This includes neural networks on normalized static counts, random forests over LLVM IR-instrumented traces (including cache and branch sim), and GNNs on full plan graphs or quantum circuits. These achieve strong accuracy at scale on test data (Kumar, 2021, Xu et al., 17 Mar 2025, Wu et al., 4 Mar 2024, Ma et al., 23 Nov 2024).

2. Mathematical and Algorithmic Foundations

ETE methodologies instantiate a variety of formal models:

• Cost Model Calibration: Many ETEs begin with a static cost model, mapping each program component (instruction, basic block, operator) to a symbolic cost, and then fit model parameters to observed run times. For example, the per-edge cost $w_e$ in loop-free code is obtained from a minimal set of basis-path timing measurements using a linear program (Bundala et al., 2015).
• Verification and Tight Bounding: In verification-oriented ETEs, the cost semantics are embedded in the operational semantics of a (core) language, and Hoare-style logic is extended to include timing assertions and invariants. These result in tight, sound execution-time verification conditions, automatically dischargable via SMT/first-order proof (Silva et al., 2022).
• Hierarchical and Cascaded Models: Stage predictor for Amazon Redshift composes a three-level cascade—hashed-execution-time cache, local instance-specific Bayesian XGBoost ensemble (mean/variance, uncertainty-aware), and zero-shot GCN over the global fleet—router-directed by cost and prediction uncertainty (Wu et al., 4 Mar 2024).
• Analytical–Statistical Stacking: ANNETTE and its variants estimate DNN/inference latency by stacking analytical roofline models with learned utilization regressors and mapping models, achieving high rank-fidelity with minimal per-network measurements (Wess et al., 2021).
• Cycle-Accurate Simulation: For reconfigurable hardware (CGRA), ETEs simulate instruction-by-instruction cycles accounting for per-micro-op, decode, memory, and data dependency delays, employing precise max-over-PEs/sum-over-instructions timing recurrence (Aspros et al., 2 Apr 2025).

3. Domains and Application Scenarios

ETE use cases span mainstream computing areas:

• Hard Real-Time and Safety Critical Systems: ETEs determining WCET or probabilistic bounds underpin task scheduling, mission-critical code audits, and allocation of execution-time budgets in mixed-criticality systems (Khelassi et al., 2023).
• Compiler Optimization and Parallelization: Static and profile-calibrated ETEs provide function cost bounds for code partitioning, task granularity analysis, and cross-platform federation 0701108.
• Databases and Query Processing: ETEs, both uncertainty-aware analytical (Propagating selectivity/cost-unit variance) and ML-based (plan cache/local/global cascades), improve admission control, query scheduling, and resource allocation for large cloud datawarehouse platforms (Wu et al., 2014, Wu et al., 4 Mar 2024).
• Neural Architecture Search and Hardware-Aware ML: Layer-mapped and mapping-mixed ETEs predict DNN/network inference latency—without full deployment or microarchitectural access—supporting design space pruning in accelerator-aware NAS (Wess et al., 2021).
• Quantum Computing: ETEs for quantum circuits employ graph-transformer models over circuit DAGs plus global scalar descriptors to provide R^2 > 0.90 simulation/hardware fit, guiding program optimization and job prioritization on scarce quantum platforms (Ma et al., 23 Nov 2024).

4. Empirical Accuracy, Uncertainty, and Limitations

ETE validation employs canonical metrics: absolute percentage error (APE), MAE, RMSE, Q-error, rank-correlation (fidelity), or (for probabilistic ETEs) KL-divergence and CDF sup-norm. Notable results include:

• PrETi: RF-based LLVM IR ETE reaches APE ≈ 12% on real-world test sets, outperforming prior methods by 5.4 pp (Xu et al., 17 Mar 2025).
• Stage (Redshift): Achieves a 20.3% reduction in query latency and 3× lower median error relative to incumbent baselines, with sub-ms overhead (Wu et al., 4 Mar 2024).
• ANNETTE: Mixed model MAPE of 3.47%–7.44% and ρ ≈ 0.99 on benchmarked NNs; microkernel layer errors ~10% (Wess et al., 2021).
• Probabilistic models: OLL-GG and Exponentiated Weibull fit task runtime data best in 75%+ of test cases; advanced c-location estimation methods reduce fit cost by 2× with equivalent likelihood (Saldanha, 2020).
• Heuristic Budgeting: VWCET-driven heuristics yield on-budget completion probabilities within 5–10% of the combinatorial optimum, with actual overrun ratios matching predicted values on embedded benchmarks (Khelassi et al., 2023).

Significant limitations include: platform or model tuning sensitivity, dataset bias, cold-start for never-seen programs, edge-case amortization in probabilistic tails, and retraining costs for evolving code or hardware. Some models (e.g., Stage global, ANNETTE full-benchmark) entail substantial up-front data acquisition.

5. Implementation, Integration, and Practical Considerations

ETE deployment pipelines reflect the target system's operational requirements:

• IDE Integration: Real-time feedback of BCET/ACET/WCET at the line or block level, driven by code sequence recurrence models, enables developer-in-the-loop design, as in industrial control IDE plug-ins (Stattelmann et al., 2014).
• Toolchain Adaptivity: Profiling-based systems (CiaoPP, TimeBill) require recalibration under hardware/firmware changes; ML-based ETEs are generally retrain-on-drift or incorporate online incremental updates, with fallback mechanisms for out-of-sample inputs 0701108.
• Scheduler Integration: Probabilistic and heuristic ETEs are plugged into scheduling algorithms (EDF, RM, stochastic-makespan minimization) for upfront feasibility, budget, or assignment optimization (Saldanha, 2020, Khelassi et al., 2023).

Computation and memory cost are often cited. For example, Stage’s hierarchical cache/local/global logic achieves amortized inference cost ≪ 1 ms, orders of magnitude below even short OLAP queries (Wu et al., 4 Mar 2024). CGRA ETEs avoid slow post-synthesis RTL simulation via parameterized, vectorized, event-driven Python models accurate to ≤10% (Aspros et al., 2 Apr 2025).

6. Advancements, Domain Shifts, and Future Prospects

Recent ETE research demonstrates domain-adaptive and hierarchical modeling, joint analytical/ML stacking, more explicit uncertainty quantification, and fine-grained feature exploitation (e.g., cache, branch, and quantum-circuit structure). Plausible future research vectors include:

• Domain-specific adaptation via hybrid factorization or transfer learning to new program classes or hardware.
• Integration with scheduling and resource managers for full stochastic (risk-aware) and robust online scheduling (Saldanha, 2020, Khelassi et al., 2023).
• Extension of ETEs to non-traditional computing substrates (quantum, reconfigurable nanoscale arrays), utilizing graph/transformer-based architectures (Ma et al., 23 Nov 2024, Aspros et al., 2 Apr 2025).
• Adaptive, uncertainty-aware feedback into real-time schedulers and design-space explorers, with error propagation integrated into control logic (Wu et al., 2014, Xu et al., 17 Mar 2025).
• Co-optimization of execution time, power, and energy in early-stage design via joint ETE/EPE (energy prediction estimator) frameworks (Aspros et al., 2 Apr 2025).

Executions Time Estimators are critical enablers of the shift toward data-driven, ML-augmented, and statistically robust system design and operation. Their continued evolution is closely tied to advances in program analysis, system modeling, ML, and scheduling theory.