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?

Connecting dispatch, clinical risk, response times and spatial allocation to understand system pressure and patient safety.

Explore the system Doctoral thesis · 2026

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×

Illustrative queue accumulation

More bufferOver capacity

Dashed: unloaded reference

Incoming patients and pass-through are illustrative system-level signals, not individual clinical outcomes.

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.

Queue pressure: 15
Readiness margin: 66
Tail-delay risk: 17

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.

Why 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 speed to system behaviour

Response time emerges from dispatch, triage, workload, geography, availability, call handling and travel.

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.

Choose your path

I am a…

A patient’s journey · about 45 seconds

The queue is a virtual waiting room.

A general care pathway · no patient data or clinical advice.

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.

The emergency call

The patient waits

Waiting remains part of the care pathway: uncertainty and urgency may change before an ambulance arrives.

The situation is reassessed

New information becomes available. In this scenario, the dispatcher reassesses the situation and reviews the allocation decision.

The first EMS contact

The crew assesses the patient on scene. The system must support this patient while preserving readiness for the next emergency.

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

Concurrent demand40LowerHigherAvailable capacity85LowerHigherSpatial allocation75ConcentratedDistributed

Step 3 · See what happens

Queue pressureStable

15 / 100

Readiness marginStable

66 / 100

Tail-delay riskStable

17 / 100

What this means in the model

Stable conditions

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×

Illustrative queue accumulation

More bufferOver capacity

Dashed: unloaded reference

Incoming patients and pass-through are illustrative system-level signals, not individual clinical outcomes.

Deeper deformation and a continuous shift from teal through amber to rose show increasing illustrative strain.

Refine conditionsWeather and operating contextContext load18

Traffic intensityOutside temperature8 °CMildSeasonPrecipitation typePrecipitation intensityRoad surfaceDay typeVisibility10 km0.2—20 km

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

In 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
Key findings: Queue pressure · Readiness margin · Tail-delay risk

All studies

Four studies. One evidence chain

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 reviewed
Stewarding scarce response capacity
Explore study 01
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 01
Resource allocation / waiting
Peer reviewed
Breathing emergencies and nonlinear risk
Explore study 02
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 02
First EMS assessment
Preprint · not peer reviewed
Infectious presentations and concordance
Explore study 03
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 03
System response-time distribution
Peer reviewed
Understanding EMS response times
Explore study 04
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

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.

Doctoral thesis & publications

Doctoral thesis · 2026 Peer-reviewed publications Research in progress

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 collaboration

EMS & health-system development

Explore readiness, allocation and patient safety in your system.

Start a conversation

Speaking & media

Discuss a conference contribution, interview or research briefing.

Get in touch

Peter Hill · peter.hill@ki.se

Karolinska Institutet profile LinkedIn

References & research resources

Bring the evidence into teaching, research and conversations about prehospital care. Reference files include the thesis, three journal articles and one preprint.

All references · RIS / EndNote All references · BibTeX Follow publications · RSS

Peer-reviewed publications

Doctoral thesis · 2026

Hill P. Adaptive emergency medical services allocation: crafting the patient safety net in prehospital emergency care. Stockholm: Karolinska Institutet; 2026. doi:10.69622/31262914

Preprint · not peer reviewed

Hill P, et al. Concordance Between Dispatch Suspicion, On-Scene Phenotype, and Time Sensitive Triage in Prehospital Infectious Presentations: A Retrospective Machine-Learning Study. Research Square. 2026. doi:10.21203/rs.3.rs-7651316/v1

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.