Pooled Testing under Congestion: Operational Scaling Laws for Pool-Size Selection
Abstract
Classical pooled-testing rules choose pool sizes to reduce the number of tests. In practice, however, samples arrive over time, pools take time to form, testing capacity is finite, and positive pools create bursts of follow-up work. These operational features can make the test-efficient pool size far from the delay-efficient one. We formulate pooled testing with stochastic arrivals and finite testing capacity as a queueing system, and derive exact performance representations and asymptotic scaling laws for fixed-batch Dorfman testing and a dynamic two-threshold policy. The analysis reveals three distinct design regimes. When test usage is the main concern, the classical Dorfman rule is recovered and the optimal pool size scales with the inverse square root of prevalence. When delay accumulated while the laboratory is busy testing another batch matters, positive pools create service-time variability that grows more rapidly with pool size than the mean retesting burden, and the optimal scale shifts to the inverse cube root of prevalence. When waiting to assemble a pool is itself costly, the optimal fixed pool size remains bounded even as prevalence becomes very small. Under severe capacity scarcity, congestion remains relevant at the classical Dorfman scale: the square-root law survives, but with a capacity-dependent constant. Dynamic pooling separates two operational decisions that fixed pool sizes conflate. A lower threshold determines when routine testing should begin, while an upper threshold limits pooling when backlog is high. The lower threshold follows the cube-root scale, whereas the upper threshold primarily acts as congestion control. The results show how prevalence, capacity, and delay jointly determine pooling decisions and explain why operationally optimal pools can be much smaller than those suggested by test-efficiency calculations alone.
Related
- An operational spatiotemporal prediction framework for sector congestion in air traffic management
- Deciding When to Decide: Testing Operational Suboptimality Under Distributional Shift
- Convergence-Aware Pareto Selection of Covariate Scaling Transformations for Markov Deterioration Hazard Models: Evidence from Bridge Inspection Data
- Selection-Aware Stress Testing for Interactive Agents
- Testing Group Differences in Network Models using Bayesian Model Selection: A Tutorial
BibTeX
@misc{dimitriou2026pooled,
title = {{Pooled Testing under Congestion: Operational Scaling Laws for Pool-Size Selection}},
author = {Ioannis Dimitriou and Johan van Leeuwaarden},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37729},
eprint = {2610.37729},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37729},
}
RIS
TY - UNPB
TI - Pooled Testing under Congestion: Operational Scaling Laws for Pool-Size Selection
AU - Ioannis Dimitriou
AU - Johan van Leeuwaarden
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37729
UR - https://arxiv.org/abs/2610.37729
AB - Classical pooled-testing rules choose pool sizes to reduce the number of tests. In practice, however, samples arrive over time, pools take time to form, testing capacity is finite, and positive pools create bursts of follow-up work. These operational features can make the test-efficient pool size far from the delay-efficient one. We formulate pooled testing with stochastic arrivals and finite testing capacity as a queueing system, and derive exact performance representations and asymptotic scaling laws for fixed-batch Dorfman testing and a dynamic two-threshold policy. The analysis reveals three distinct design regimes. When test usage is the main concern, the classical Dorfman rule is recovered and the optimal pool size scales with the inverse square root of prevalence. When delay accumulated while the laboratory is busy testing another batch matters, positive pools create service-time variability that grows more rapidly with pool size than the mean retesting burden, and the optimal scale shifts to the inverse cube root of prevalence. When waiting to assemble a pool is itself costly, the optimal fixed pool size remains bounded even as prevalence becomes very small. Under severe capacity scarcity, congestion remains relevant at the classical Dorfman scale: the square-root law survives, but with a capacity-dependent constant. Dynamic pooling separates two operational decisions that fixed pool sizes conflate. A lower threshold determines when routine testing should begin, while an upper threshold limits pooling when backlog is high. The lower threshold follows the cube-root scale, whereas the upper threshold primarily acts as congestion control. The results show how prevalence, capacity, and delay jointly determine pooling decisions and explain why operationally optimal pools can be much smaller than those suggested by test-efficiency calculations alone.
ER -