Introduction

‘As before the pandemic, emergency departments have once again become the catch-all for much of the health system’s overflow. As the last resort, they are themselves under strain, being called upon not only for genuine emergencies, but also by patients unable to secure a timely GP appointment and by those with chronic conditions not receiving regular medical follow-up care .’

This statement is from the report entitled ‘L’accueil et le traitement des urgences à l’hôpital’(Hospital Reception and Management of Emergency Cases), published by the French Court of Auditors (Cour des Comptes) in November 2024. The report is alarming, describing a healthcare system under severe strain due to overstretched departments struggling to cope with ever-increasing demand. To resolve this issue, the Court of Auditors’ report stresses the urgent need to review the patient pathway prior to attendance at the emergency department (ED, commonly known as A&E in the UK, for Accidents and Emergencies). Indeed, departments that care for patients requiring unscheduled treatment are complex systems, dealing with unpredictable demand and limited resources, often resulting in long waiting times. These situations have a direct impact on quality of care, patient safety, and operational efficiency.

This SKEMA Publika policy paper draws on the work of Benjamin Legros to show how mathematical tools and models can be used to analyse, understand and optimise queue management in emergency departments, while also taking into account human and organisational factors. It explores the application of queueing theories and other mathematical approaches to address the challenges of emergency departments by modelling patient arrival processes, analysing risk aversion, proposing patient prioritisation strategies, and emphasising staff training and the role of call centres.

The matter examined in this policy paper is highly topical, given the budgetary pressures faced by the French state and, in particular, by public hospitals. Statistics from INSEE, the French National Institute of Statistics and Economic Studies, show that in 2022, la Sécurité Sociale, France’s social security system, covered 80% of the French population’s healthcare spending . This corresponds to 11.9% of GDP spent on healthcare . Healthcare is therefore one of the state’s largest areas of expenditure, and it also places a heavy burden on the public deficit. According to estimates by the Fédération Hospitalière de France (the Hospital Federation of France), hospitals were running a deficit of 3.4 billion euros in 2024 . This policy paper is also situated within a political context in which the government is seeking to reduce public debt to 3,305.3 billion euros (2024) and is preparing a fiscal consolidation plan aimed at achieving €40 billion in savings by 2026. Our analysis aims to provide inspiration for these efforts to reduce expenditure, by offering concrete public-policy solutions to ease congestion in emergency departments, thereby contributing to the broader improvement of the French healthcare system. In particular, it challenges the notion that the congestion problem can be resolved solely by allocating more material, financial and human resources. Instead, we present an alternative perspective, arguing that it is more cost-effective to rethink task routing and staff roles, highlighting the value of integrating mathematical models and new digital technologies into this reflection. At the heart of our analysis lies the following question:

• In a difficult budgetary context, how can patient flow management in emergency departments be optimised?

In part one, we explore the theoretical foundations of queueing in emergency departments. Part two examines how game theory can shed light on patient behaviour. In Part three, we focus on the critical issue of patient prioritisation. Part four analyses the role staff training can play in optimising patient flow, while Part five looks at how call centres could help manage patient flow more effectively. Finally, in Part six, we outline the challenges and future possibilities arising from task routing in emergency departments. In addition, this study includes comparisons with emergency systems in other countries, in order to draw inspiration from the public policies in place there and provide concrete recommendations for improving access to care in French emergency departments.

Recommendations

Use new digital technologies:

Encourage human–machine cooperation by having AI perform an automatic pre-triage that redirects patients before they present at the ED, smooths patient flow, improves the accuracy of predictions, and reduces the impact of risk aversion.
Expand the use of telemedicine and digital health solutions by introducing self-service registration and payment kiosks.
Use digital twins to dynamically test organisational and strategic changes and evaluate their hypothetical impact on hospital performance.

Train hospital staff:

Increase the versatility and efficiency of clinical and non-clinical staff by training them to optimise patient flow and length of stay.
Develop a continuing professional development (CPD) system for training in emergency medical skills to support clinical staff during periods of congestion. This would create shared competencies among all staff, improving cooperation.
Improve stress management through scenario-based training. The development of interactive simulation platforms for training and planning could also be considered.

Reorganise:

Implement a system to triage patients at the ED entrance. However, it should be noted that a key limitation of this approach is distinguishing between a patient’s actual state and their perceived state.
Facilitate the construction of local hospitals providing basic care alongside referral hospitals equipped with specialised facilities and advanced care.
Factor into the decision-making process the risk of staff attrition related to stress and burnout. To mitigate these, optimise schedules and assignments to prevent unplanned overtime for clinical staff.
Facilitate information transfer protocols between call centres and the ED through an integrated information system.

Introduce binding and non-binding incentives:

Implement binding incentives, such as symbolic admission fees, to discourage non-essential visits.
Implement non-binding incentives to help patients understand the negative externality created when they decide to join the queue. In conditions of congestion, this decision can place undue strain on hospital resources. One approach could be to raise patient awareness through poster campaigns displayed at ED entrances. A second could involve media campaigns. A third could be to set up an online booking system informing patients of the additional waiting time generated by their arrival.