Handling emergency calls: tropical geometry for emergency services in Paris

Prior to the reforms, the police and the fire brigade in Paris managed five separate emergency call handling centres in Paris and its inner suburbs . The police had one centre per département (75, 92, 93 and 94), receiving calls made to the emergency number 17. The fire brigade had an urban centre receiving all calls made to the emergency numbers 18 and 112.

Both under the control of the Paris Police Prefecture, the two organisations were housed withinthe same platform.This was to meet three objectives:

• to modernise the handling of emergency calls, of benefit first and foremost to the population in the area
• to render more secure the response procedure for joint call-outs from the minute calls are received
• to optimise resources through pooling

Faced with a rise in the number of emergency calls, the Prefecture also introduced a two-tier response system: each call is initially handled by a “neutral” operator , who then filters and qualifies the call depending on its severity prior to transferring it, where necessary, to a skilled specialist (fire brigade or police).

This reorganisation, introduced gradually since 2016, is now continuing, with contributions made by a number of researchers from Inria:

• Stéphane Gaubert , head of the Tropical research team (a joint undertaking involving the Inria Saclay - Île-de-France research centre and the École Polytechnique), specialists in tropical geometry - a branch of mathematics used to study waiting times and congestion.
• Xavier Allamigeon , a member of the Tropical team
• Philippe Robert , an expert in probability theory applied to networks at the Inria research centre in Paris

A mathematical model for simulating all scenarios

The researchers were contacted by Régis Reboul, the project director in charge of these reforms (answering to the Prefect Secretary-General for the Paris Police Prefecture Administration), and by lieutenant colonel Stéphane Raclot, his deputy, in 2014.

It was necessary to simulate all possible scenarios, from the simplest to the worst cases of congestion, in order to test the effectiveness of the platform,

explains Stéphane Gaubert.

“With a number of students from the École Polytechnique and Vianney Boeuf, a PhD student from the École des Ponts ParisTech, we built a complex mathematical model representing how the system would work.”

This helped to consolidate the project prior to it becoming a reality, particularly in terms of sizing: “We managed to evaluate the maximum number of calls that could be handled, all the whileensuring a reduced waiting time, depending on the number of people mobilised on the platform , adds Stéphane Gaubert. We were thus able to demonstrate the minimum staff levels required, for both first and second-tier response, in order to guarantee fluidity with regard to call handling.”

The researchers also showed that the new system offered a greater level of protection for serious emergencies (heart attacks, armed robbery, etc.). In the event of a significant peak in the volume of calls, the fact that an operator is used for filtering helps to ensure that the most serious cases are passed on as a priority to specialist experts. This is a speedy process, with less time taken up by nuisance calls, which are now filtered at the first-tier.

The benefits of adding a 30-second filtering stage, including in nominal mode

In 2018, during work carried out with two students from the École Polytechnique, Célia Escribe and Céline Moucer, the benefits outside of call peaks were shown. If there is no congestion, the waiting time to speak to an expert is extended by 30 seconds, as a result of the response level being added. However, this time is not lost: it gives the first-tier operator, using a carefully-prepared questionnaire, the opportunity to gather all of the information needed in order for the expert to be able to handle the call effectively and to enable the rapid mobilisation of response teams.

The new system also helps boost performance levels without increasing the total number of people on the platform, owing to the way in which first-tier operators are pooled and the fluxing of pick-up for incoming calls.

We are in the process of deploying an information system capable of securing all data exchanges within this two-tier set-up

announced lieutenant colonel Stéphane Raclot.

“Among other benefits, platform managers will be notified each time one of the indicators identified during the operational research carried out with Inria and the École Polytechnique exceeds a set threshold. This could be a rise in the waiting time between the two response tiers, for example. The protocols designed to limit the risk of congestion can be adapted to such thresholds, calling for reinforcements or modifying the rules for transferring calls. These points have since been objectively appraised, with a greater degree of clarity and acuity. Until now, the application of these procedures and staff management often depended on the professional experience of the managers in charge of the different emergency call handling centres.”

Extending the study to calls made to the ambulance service

The scope of the work is now being broadened, with “Health” taken into account within the call handling process , in cooperation with Assistance Publique - Hôpitaux de Paris ’s four ambulance services (SAMU 75, 92, 93 and 94).

The calls that they receive on 15 “health” have specific characteristics requiring a chain response, from the call being qualified right through to sizing and the monitoring of the response by the regulating doctor. Some calls are also made via the universal emergency number 112 or via the emergency numbers 17 and 18, which are picked up by the unified platform outlined previously.

A PhD student from the team, Marin Boyet, is carrying out extensive research on the data and is extending the models in order to help medical teams identify the most relevant scenarios for ensuring that patients are dealt with quickly and securely during their care pathway, from the minute their calls are received by the platform's first-tier operators. Extending the study to calls made to the ambulance service.