Stopping Criteria in Simulation: A Survey of Methods, Applications, Challenges, and Future Directions

Abstract

Determining when accumulated simulation output is sufficient for an inference or decision is a recurring problem because premature termination can compromise statistical properties, whereas unnecessary continuation consumes computational and sampling resources. This survey examines data-dependent termination under uncertainty: operational rules that update evidence from sequential observations or batches and decide whether acquisition should stop or continue. A protocol-driven search of Scopus and Web of Science, covering 2015-2025 through four targeted strategies, identified 54 primary studies presenting 95 operational contributions, defined as distinct stopping procedures or operationally distinct variants. Reporting was informed by PRISMA 2020 and PRISMA-S. The contributions were organized into five families according to their terminal rationale: precision or uncertainty sufficiency, discrete-decision sufficiency, risk or loss sufficiency, operational-state sufficiency, and resource-aware acquisition and stopping. Among the 95 contributions, demonstrated evidence was documented for finite-sample behavior in 82, comparison with alternative rules in 66, robustness in 17, computational or scalability assessment in 47, and implementation availability in 7. A conditional practitioner map relates nine application constraints to the five families without prescribing a universal rule. The synthesis identifies two cross-family gaps concerning external evidence and changing data streams, together with a corpus-bounded application gap in defense constructive simulation.

@article{nunes2026stopping,
  author = {Nunes, Artur Ligieri and Moreira, Guilherme and Dantas, Joao P. A. and Dias, Luiz Alberto Vieira},
  title = {{Stopping Criteria in Simulation: A Survey of Methods, Applications, Challenges, and Future Directions}},
  journal = {IEEE Access},
  year = {2026},
  doi = {10.1109/ACCESS.2026.3744986},
  url = {https://doi.org/10.1109/ACCESS.2026.3744986}
}