Modeling Yellow and Red Alert Durations for Ambulance Systems
Bibliographic record
Abstract
Emergency systems are designed to almost always have enough capacity to respond to emergencies. However, capacity shortage periods do occur and these systems need to recover quickly. In this study, we apply queueing models and study whether it is better for an emergency system to add or to expedite servers, in order to quickly recover from a capacity shortage period. We focus on emergency medical service (EMS) systems and use Erlang loss models to study Red Alerts (when all ambulances are busy) and Yellow Alerts (when the number of available ambulances falls below a threshold). We analyze two loss models: one with Markovian state‐dependent service rates and one with generally and independently distributed service times. We validate the two models against EMS data sets from two cities. Despite the fact that the distribution of ambulance service times is a mixture of lognormal distributions, which is far from being exponential, we find that the loss model with Markovian state‐dependent service rates provides a better representation of empirical Yellow and Red alert statistics. We build on the model with state‐dependent rates and use the theory of absorbing Markov chains to quantify the impact of adding or expediting ambulances, with respect to two performance measures: (i) the duration of alert periods, and (ii) the number of lost calls. This quantification helps EMS staff (dispatchers and supervisors) to make better decisions to avoid, and to recover from, alert periods. For example, staff should not wait until a Red Alert before adding ambulances, which is a common practice, because the expected number of lost calls rapidly increases as the number of available ambulances at the action epoch decreases.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".