Baccelli's research is at the interface between mathematics (probability theory, stochastic geometry, dynamical systems) and communications (information theory, wireless networks, network science).
His work with P. Brémaud on the stationary-ergodic framework for queuing networks represents such networks as functionals of point processes on the real line. This led to mathematical tools which are now commonly used in applied probability and in the communication network literature.
Jointly with G. Cohen, J.P. Quadrat and G.J. Olsder, he contributed to the development of an algebraic theory for the dynamics of networks, the so-called (max, plus) algebra. This impacted several fields of engineering (network calculus) and mathematics (tropical geometry).
He is best known for contributions to stochastic geometry. His results on the Poisson-Voronoi model, the Poisson-Shannon model, and the Poisson-Voronoi-Shannon model laid the foundations of the representation of communication networks as functional of point processes in the Euclidean space. This led to wireless stochastic geometry, initially developed with B. Blaszczyszyn, which is now commonly used in the communication network literature.
His current research interests are in stochastic geometry in high dimension, in the theory of stationary point processes, and in the mathematics of unimodular random graphs.