From speed to system behaviour
Response time emerges from dispatch, triage, workload, geography, availability, call handling and travel.
Choose how to explore
Prehospital emergency care · Patient safety
Crafting the
patient safety net.
How should ambulance systems allocate scarce capacity when several patients need help at the same time?
Research on ambulance allocation, waiting, system pressure and patient safety.
THE EMS SAFETY NET
The safety net responds
Choose a scenario to see the system change.
Relative demand / capacity0.47×
Capacity bufferCapacity boundary: 1.00×
More bufferOver capacity
Dashed: unloaded reference
Illustrative model · no live data
Waiting time does not carry the same risk for every patient. Colour and the growing ring illustrate different time sensitivities, not predicted clinical outcomes. Figures are representative, not actual counts.
People represent available support across EMS professions; fewer figures show reduced reserve as pressure rises, not actual staffing levels. Ambulances illustrate movement through the system, not real vehicles or routes.
Stable Illustrative system state · indices 0–100
- Queue pressure
- 15 / 100
- Readiness margin
- 66 / 100
- Tail-delay risk
- 17 / 100
There are enough available ambulances to absorb new demand. The system retains reserve capacity.
Change the system
Demand deepens the net. Capacity keeps it taut. Uneven allocation leaves some areas less supported.
Illustrative model outputs
- Queue pressure
- Demand pushing against available service
- Readiness margin
- Capacity left for the next emergency
- Tail-delay risk
- Very long waits in this illustrative model
Illustrative model · no live dataExplore the system
Illustrative indices from 0 to 100. These are not percentages, patient risks or forecasts; the weights are not estimated from the studies.
In brief
EMS is a dynamic patient safety net.
Dispatchers described balancing current patient needs with readiness for the next emergency.
Stewarding scarce response capacityRelationships between response time and clinical urgency varied with patient characteristics; the exploratory model was not validated for individual prediction.
Breathing emergencies and nonlinear riskResponse-time distributions varied with system conditions. Typical response times alone can conceal long waits.
Understanding EMS response times
These studies describe professional experience and observational associations. They do not demonstrate that a particular allocation policy improves clinical outcomes. The interactive model is illustrative, not validated for individual prognosis.
Policy brief — Research summaryWhy this matters
A safety net is more than a response-time target.
Speed matters. But it cannot, on its own, describe patient safety.
Ambulance systems operate with uncertain information, fluctuating demand, geographic variation and finite resources. Every allocation decision shapes who receives help first, who waits and how safety margins are distributed across the system.
Explore the three principles
From queue to virtual waiting room
Queued patients require active monitoring, reassessment, escalation and organisational ownership.
From data to responsible governance
Routine EMS data can reveal patterns, provided uncertainty and interpretation boundaries remain visible.
A patient’s journey · about 45 seconds
The queue is a virtual waiting room.
A general care pathway · no patient data or clinical advice.
A patient has called for help. No ambulance is available yet. Waiting is already part of the care pathway.
- Emergency call
- Dispatch assessment
- Queue / waiting
- Possible reassessment
- Resource allocation
- EMS arrival
- First EMS assessment
The emergency call
A person calls for help. The dispatcher receives incomplete information while several other patients also need a response. Available resources and the initial assessment shape priority and allocation.
Four studies. One question.
From dispatch decisions to clinical uncertainty and system delays. Three peer-reviewed articles and one preprint contribute different parts of the picture.
- Emergency call
Dispatch assessment
Peer reviewedStewarding scarce response capacity
Question, findings and limitations
- Research question
- How dispatchers prioritise patients, govern the queue and preserve readiness when ambulance capacity is constrained.
- Study population · Method
- Qualitative interviews with 13 emergency medical dispatchers working across 10 emergency medical communication centres; analysed using inductive content analysis.
- Key findings
- Dispatchers described a professional responsibility to steward scarce response capacity through proportionate allocation, preserved availability and coordinated system response.
- Interpretation boundaries
- The findings describe professional experience in one organisational context and should be transferred to other EMS systems with attention to local governance.
Dispatch & queue governance
BMJ Open · 2026Explore study 01Resource allocation / waiting
Peer reviewedBreathing emergencies and nonlinear risk
Question, findings and limitations
- Research question
- How response time, age and sex interact with high-risk time-sensitive triage among 132,395 breathing-problem missions.
- Study population · Method
- Retrospective observational analysis of 132,395 breathing-problem missions in Stockholm, 2017–2022. Multiple models were explored, with PD and ICE plots used to examine nonlinear relationships.
- Key findings
- Age was the most important model feature. Patients older than 60 showed complex rising HRTS probability at prolonged response times beyond two hours; discrimination was modest (AUC 0.66).
- Interpretation boundaries
- The exploratory model is not validated for patient-level prediction or dispatch automation and was based on limited variables from one region.
Patient vulnerability & waiting
BMC Medical Informatics and Decision Making · 2025Explore study 02First EMS assessment
Preprint · not peer reviewedInfectious presentations and concordance
Question, findings and limitations
- Research question
- How dispatch suspicion, on-scene phenotype and high-risk time-sensitive triage align in infectious presentations.
- Study population · Method
- Retrospective machine-learning study comparing dispatch suspicion of infection, the on-scene symptom phenotype and high-risk time-sensitive triage.
- Key findings
- The three information layers did not represent the same clinical construct; concordance changed depending on where in the care pathway infection and urgency were assessed.
- Interpretation boundaries
- This preprint has not completed journal peer review. Observational associations do not establish causal effects or operational thresholds.
Information across the care pathway
Research Square · 2026Explore study 03System response-time distribution
Peer reviewedUnderstanding EMS response times
Question, findings and limitations
- Research question
- How priority, workload, geography, weather and operational intervals shape variability and tail delays.
- Study population · Method
- Retrospective analysis of 1,144,754 EMS missions in Stockholm, 2017–2022, integrating operational, geographic and weather variables with regression and machine-learning analyses.
- Key findings
- Priority was the strongest overall feature, but workload, call reason, geography, precipitation, temperature and operational intervals interacted. Lower priorities had markedly long-tailed response-time distributions.
- Interpretation boundaries
- Traffic information was unavailable, the study was conducted in one region and predictive performance does not make the models ready for real-time deployment.
System capacity & response-time variation
BMC Medical Informatics and Decision Making · 2025Explore study 04
Choose your path
I am a…
What happens when ambulance demand approaches capacity?
Interactive systems explorer
See pressure move through the safety net.
Illustrative teaching model · no live data · not clinical decision support. Values are neither empirical findings nor patient-level predictions.
Step 1 · Choose a scenario
Step 2 · Change the system
Step 3 · See what happens
Queue pressureStable
15 / 100Readiness marginStable
66 / 100Tail-delay riskStable
17 / 100What this means in the model
Stable
Demand is well below available capacity. The model retains a readiness margin to absorb concurrent needs; local delays can still occur.
Illustrative indices · 0–100, not percentages or minutes. Display categories are not validated operational thresholds.
Relative demand / capacity0.47×
Capacity bufferCapacity boundary: 1.00×
More bufferOver capacity
Dashed: unloaded reference
Illustrative model · no live data
Waiting time does not carry the same risk for every patient. Colour and the growing ring illustrate different time sensitivities, not predicted clinical outcomes. Figures are representative, not actual counts.
People represent available support across EMS professions; fewer figures show reduced reserve as pressure rises, not actual staffing levels. Ambulances illustrate movement through the system, not real vehicles or routes.
Deeper deformation and a continuous shift from teal through amber to rose show increasing illustrative strain.
Refine conditionsWeather and operating contextContext load
Advanced analysisA/B comparison · scientific assumptions · presentation
Pressure rises sharply as demand approaches capacity. At or above the boundary, a sustained load has no finite stationary mean in the idealised infinite-queue model.
Why pressure rises nonlinearly
Theoretical referenceIn an M/M/1 queue with utilisation ρ < 1, mean queueing time is Wq = ρ / [μ(1 − ρ)]. The rise is hyperbolic as ρ approaches 1. This is a theoretical reference, not a fitted model of ambulance services.
Here r = D/C compares relative demand and capacity on the same illustrative scale; it is not measured utilisation. For r < 1, q = r/(1 − r). Context and spatial allocation modify the display indices using illustrative weights.
The indices are bounded at 100 for display. At r ≥ 1, queue pressure and tail-delay indices reach that bound and the margin is zero; this is not a finite queue forecast. The net continues to deform with excess demand. Colour and label intervals are illustrative.
Queueing theory · MIT- Core system state
- Concurrent demand · Available capacity · Spatial allocation
- Weather and operating context
- Traffic intensity · Outside temperature · Precipitation type · Road surface · Visibility · Day type
- Illustrative model outputs
- Queue pressure · Readiness margin · Tail-delay risk
What this means for EMS systems
Use the evidence to frame system questions, then evaluate changes in the local service.
Protect readiness
Follow available capacity and queue pressure together. Preserve room to absorb simultaneous needs, especially close to capacity.
Look beyond the typical response
Examine tail delays and geographic variation in ambulance response time. A system average can conceal where waiting accumulates.
Treat risk as dynamic
Make reassessment and ownership of waiting patients explicit. Clinical urgency can change while resources remain committed.
Evaluate resilience
Test how the system absorbs disruption and recovers readiness. Assess patient safety, distributional effects and human judgement before operational use.
RESEARCH GUIDE
Ask EMS Allocation
Explore the research through questions.
This AI research guide uses the published research, thesis and explanatory material on this site. Answers should cite their sources and distinguish evidence status. It can make mistakes and is not clinical decision support. Questions are processed by Mistral AI; do not enter personal or patient information. Research integrity
Doctoral thesis & publications
Peter Hill · Karolinska Institutet · DOI 10.69622/31262914
Research question and planned approach only. Unpublished results are not disclosed.
Research · Collaboration · Speaking
Let’s take the research further
Research collaboration
Develop research questions, methods and cross-system studies.
Discuss collaborationEMS & health-system development
Explore readiness, allocation and patient safety in your system.
Start a conversationSpeaking & media
Discuss a conference contribution, interview or research briefing.
Get in touchResearch integrity
The research is observational and explanatory. It does not provide patient-level advice or a validated real-time dispatch tool. Operational translation requires prospective evaluation, governance, human-factors design and safeguards.
Methodological limitations & research integrityReferences & research resources
Bring the evidence into teaching, research and conversations about prehospital care. Reference files include the thesis, three journal articles and one preprint.
Policy brief · Research summaryAll references · RIS / EndNoteAll references · BibTeXFollow publications · RSS
Peer-reviewed publications
- Hill P, Lederman J, Jonsson D, Bolin P, Vicente V. Stewarding scarce response capacity: an inductive qualitative interview study of emergency medical dispatchers prioritising ambulance resources. BMJ Open. 2026. doi:10.1136/bmjopen-2026-118269
- Hill P, Jonsson D, Lederman J, Bolin P, et al. Uncovering nonlinear patterns in time-sensitive prehospital breathing emergencies: an exploratory machine learning study. BMC Med Inform Decis Mak. 2025;25:205. doi:10.1186/s12911-025-03046-z
- Hill P, Lederman J, Jonsson D, Bolin P, et al. Understanding EMS response times: a machine learning-based analysis. BMC Med Inform Decis Mak. 2025;25:143. doi:10.1186/s12911-025-02975-z
Doctoral thesis · 2026
Preprint · not peer reviewed
Methodological limitations & research integrity
Exploration before deployment
The research is observational and explanatory. It does not provide patient-level advice or a validated real-time dispatch tool. Operational translation requires prospective evaluation, governance, human-factors design and safeguards.
Illustrative teaching model · no live data · not clinical decision support. Values are neither empirical findings nor patient-level predictions.
Methodological limitations & research integrity