Marin Boyet


I defended my Ph.D. thesis in applied mathematics "Piecewise affine dynamical systems applied to the performance evaluation of emergency call centers" on the 25 May 2022. This work took place at CMAP, École Polytechnique, and INRIA Saclay, under the supervision of Stéphane Gaubert and Xavier Allamigeon.

We focused in this work on piecewise-affine and switched dynamical systems. These typically arise from real-life organizations modelled by means of Petri nets, a popular formalism in discrete-event systems. Relying on techniques from stochastic control, combinatorics and nonlinear (max-plus) geometry, we characterized the behaviour of the trajectories of these dynamics. We applied our results to the case of emergency call centers, describing congestion phases of different architectures, computing minimum staffing numbers and bouding the time needed to absorb a peak of calls.

We worked in partnership with the Préfecture de Police de Paris (operating the police and firebrigade emergency platform) and the Services d'Aide Médicale Urgente (organizing the emergency response for health-related calls) of Paris area.

This research was funded by INRIA and AID.


Ph.D. manuscript
  • M. Boyet, Piecewise affine dynamical systems applied to the performance evaluation of emergency call centers, 2022. [local file]

  • X. Allamigeon, M. Boyet, S. Gaubert. Piecewise Affine Dynamical Models of Timed Petri Nets - Application to Emergency Call Centers, 2021, Fundamenta Informaticae. [Journal, arXiv, hal]

  • S. Gaubert, M. Akian, X. Allamigeon, M. Boyet, B. Colin, T. Grohens, L. Massoulié, D. Parsons, F. Adnet, É. Chanzy, L. Goix, F. Lapostolle, É. Lecarpentier, C. Leroy, T. Loeb, J.-S. Marx, C. Télion, L. Tréluyer, P. Carli. Understanding and monitoring the evolution of the Covid-19 epidemic from medical emergency calls: the example of the Paris area , 2021, Comptes rendus mathématiques de l'académie des sciences. [Journal,arXiv, hal]

  • The COVID-19 APHP-Universities-INRIA-INSERM Group, Early indicators of intensive care unit bed requirement during the COVID-19 epidemic: A retrospective study in Ile-de-France region, France, 2021, PLOS One. [Journal, pubMed, arXiv]

  • X. Allamigeon, M. Boyet, S. Gaubert. Computing Transience Bounds of Emergency Call Centers: a Hierarchical Timed Petri Net Approach, 2022, to appear in the proceedings of the Petri Nets 2022 conference. [arXiv]

  • M. Akian, X. Allamigeon, M. Boyet, S. Gaubert. A convex programming approach to solve posynomial systems, 2020, Proceedings of the ICMS 2020 conference. [arXiv, hal]

  • M. Akian, X. Allamigeon, M. Boyet, S. Gaubert. The colorful interior of convex bodies and its tropical analog, 2019, poster presented at the SIAM AG 2019 conference. [PDF]

Technical reports
  • X. Allamigeon, M. Boyet, S. Gaubert, Études des données de téléphonie (février 2019), modélisation et premières indications de dimensionnement, 2020, internal reports delivered to the four SAMU of AP-HP.

  • X. Allamigeon, M. Boyet, B. Colin, S. Gaubert, Optimisation de la performance de centres de traitement d'appels d'urgence, 2021, comissionned by the Institut des Hautes Études du Ministère de l'Intérieur. [PDF (in French, soon)]


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  • Physical address: Office 2011, CMAP, École Polytechnique, 91128 Palaiseau Cedex, France.