Francois Baccelli

• Doctor of Philosophy
• Directeur de recherche at National Institute for Research in Computer Science and Control

Reconfigurable intelligent surfaces (RISs) enhance wireless communication by creating engineered signal reflection paths in addition to direct links. This work presents a stochastic geometry framework using point processes (PPs) to model multiple randomly deployed RISs conditioned on their associated base station (BS) locations. By characterizing a...

Clustering is a widely used technique in unsupervised learning to identify groups within a dataset based on the similarities between its elements. This paper introduces three new hierarchical clustering models, Clustroid Hierarchical Nearest Neighbor (\(\mathrm{CHN}^2\)), Single Linkage Hierarchical Nearest Neighbor (\(\mathrm{SHN}^2\)), and Hausdo...

Even when driven by the same stimulus, neuronal responses are well-known to exhibit a striking level of spiking variability. In-vivo electrophysiological recordings also reveal a surprisingly large degree of variability at the subthreshold level. In prior work, we considered biophysically relevant neuronal models to account for the observed magnitu...

Even when driven by the same stimulus, neuronal responses are well-known to exhibit a striking level of spiking variability. In-vivo electrophysiological recordings also reveal a surprisingly large degree of variability at the subthreshold level. In prior work, we considered biophysically relevant neuronal models to account for the observed magnitu...

Even when driven by the same stimulus, neuronal responses are well-known to exhibit a striking level of spiking variability. In-vivo electrophysiological recordings also reveal a surprisingly large degree of variability at the subthreshold level. In prior work, we considered biophysically relevant neuronal models to account for the observed magnitu...

Reconfigurable intelligent surfaces (RISs) are a promising technology for enhancing cellular network performance and yielding additional value to network operators. This paper proposes a techno-economic analysis of RIS-assisted cellular networks to guide operators in deciding between deploying additional RISs or base stations (BS). We assume a rela...

This paper defines a new model which incorporates three key ingredients of a large class of wireless communication systems: (1) spatial interactions through interference, (2) dynamics of the queueing type, with users joining and leaving, and (3) carrier sensing and collision avoidance as used in, e.g., WiFi. In systems using (3), rather than direct...

In vehicle-to-everything (V2X) communications, roadside units (RSUs) play an essential role in connecting various network devices. In some cases, users may not be well-served by RSUs due to congestion, attenuation, or interference. In these cases, vehicular relays associated with RSUs can be used to serve those users. This paper uses stochastic geo...

In practice, low Earth orbit (LEO) and medium Earth orbit (MEO) satellite networks consist of multiple orbits, each populated with many satellites. A widely used spatial architecture for satellites is the Walker constellation, where the longitudes of orbits are equally spaced and the satellites are periodically distributed along the orbits. In this...

La 6G est fondée sur l’utilisation de plusieurs nouveaux types d’éléments de réseau, de fréquences et d’architectures. La maîtrise de la complexité de la couverture radio qui en résulte requiert le développement de nouveaux outils de conception et d’analyse. Cet article a pour but de décrire les principes de l’approche de ces questions par la géomé...

Cet article, qui est issu du rapport de l’Académie des Sciences « Grandes constellations de satellites : enjeux et impacts », a pour objectif de décrire l’organisation, les fonctionnalités et les perspectives des réseaux de communications utilisant des constellations de satellites.Il se concentre sur les fonctionnalités de communications haut débit...

The Doeblin graph of a countable state space Markov chain describes the joint pathwise evolutions of the Markov dynamics starting from all possible initial conditions, with two paths coalescing when they reach the same point of the state space at the same time. Its bridge Doeblin subgraph only contains the paths starting from a tagged point of the...

In this paper, we study a multiclass spatial birth-and-death (SBD) processes on a compact region of the Euclidean plane modeling wireless interactions. In such a setup, users arrive at a constant rate and leave at a rate inversely proportional to a shot noise created by interfering users in the network. The novelty of this work lies in the addition...

This work develops an analytical framework for downlink low Earth orbit (LEO) or medium Earth orbit (MEO) satellite communications, leveraging tools from stochastic geometry. We propose a tractable approach to the analysis of such satellite communication systems, accounting for the fact that satellites are located on circular orbits.We accurately i...

This paper uses the theory of point processes and stochastic geometry to quantify the sky visibility experienced by users located in an outdoor environment. The general idea is to represent the buildings of this environment as a stationary marked point process, where the points represent the building locations and the marks their heights. The point...

We introduce a stochastic geometry dynamics inspired by opinion dynamics, which captures the essence of modern asymmetric social networks, with leaders and followers. Opinions are represented by points in the Euclidean space and the leader of an agent is the agent with the closest opinion. In this dynamics, each follower updates its opinion by halv...

Consider the following migration process based on a closed network of N queues with $K_N$ customers. Each station is a $\cdot$ /M/ $\infty$ queue with service (or migration) rate $\mu$ . Upon departure, a customer is routed independently and uniformly at random to another station. In addition to migration, these customers are subject to a susceptib...

With the growing interest in satellite networks, satellite-terrestrial integrated networks (STINs) have gained significant attention because of their potential benefits. However, due to the lack of a tractable network model for the STIN architecture, analytical studies allowing one to investigate the performance of such networks are not yet availab...

We develop an analytical framework to examine the line-of-sight (LOS) coverage area in vehicular networks with roadside units (RSU) and vehicle relays. In practical deployment scenarios, RSUs and vehicle relays are spatially correlated and we characterize this by employing Cox point processes to model the locations of RSUs and vehicle relays simult...

This work develops a novel approach towards performance guarantees for all links in arbitrarily large wireless networks. It introduces spatial regulation properties for stationary spatial point processes, which model transmitter and receiver locations, and develops the first steps of a calculus for this regulation. This spatial network calculus can...

We propose a simple analytical approach to describe the locations of low earth orbit (LEO) satellites based on a Cox point process. We develop a variable-altitude Poisson orbit process by accounting for the fact that satellites are always located on circular orbits and these orbits may have different altitudes. Then, the satellites on these orbits...

This work develops a novel approach toward performance guarantees for all links in arbitrarily large wireless networks. It introduces a spatial network calculus , consisting of spatial regulation properties for stationary point processes and the first steps of a calculus for this regulation, which can be seen as an extension to space of the class...

This work develops an analytical framework for downlink low earth orbit (LEO) satellite communications, leveraging tools from stochastic geometry. We propose a tractable approach to the analysis of such satellite communication systems accounting for the fact that satellites are located on circular orbits. We accurately characterize this geometric p...

This article presents a stochastic geometric framework to model and analyze spatially correlated blockage in a vehicular network. First, we model the vehicular obstacles as a Boolean model on a line using stochastic geometry. Then, we represent signal paths from transmitters to receivers as a graph from the transmitter point process to the receiver...

This paper proposes a cascade blockage model for analyzing the vision that a user has of a wireless network. This model, inspired by the classical multiplicative cascade models, has a radial structure meant to analyze blockages seen by the receiver at the origin in different angular sectors. The main novelty is that it is based on the geometry of o...

Consider a migration process based on a closed network of N stations with K_N customers. Each station is a ./M/\infty queue with service (migration) rate mu. Upon departure, a customer is routed at random to another station. In addition to migration, these customers are subject to an SIS (Susceptible, Infected, Susceptible) dynamics: customers are...

We study an N -player game where a pure action of each player is to select a nonnegative function on a Polish space supporting a finite diffuse measure, subject to a finite constraint on the integral of the function. This function is used to define the intensity of a Poisson point process on the Polish space. The processes are independent over the...

While roadside units (RSUs) play an essential role in vehicle-to-everything (V2X) by communicating with users, some users in congestion areas may not be well-served due to data traffic, signal attenuation, and interference. In these cases, vehicle relays can be employed to enhance the network topology to better serve those users. This paper leverag...

The Doeblin Graph of a countable state space Markov chain describes the joint pathwise evolutions of the Markov dynamics starting from all possible initial conditions, with two paths coalescing when they reach the same point of the state space at the same time. Its Bridge Doeblin subgraph only contains the paths starting from a tagged point of the...

Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of i...

This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of...

Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta$ . The first is the set of points that belong to some one-dimensional facet of the Voronoi tessellation and such...

This paper proposes a cascade blockage model for analyzing the vision that a user has of a wireless network. This model, inspired by the classical multiplicative cascade models, has a radial structure meant to analyze blockages seen by the receiver at the origin in different angular sectors. The main novelty is that it is based on the geometry of o...

This paper analyzes the use of vehicular relays as a means to extend the Line-of-Sight (LOS) coverage from roadside units(RSUs) toward users on the streets in mmWave or visible light communications. In this paper, we consider the scenario where RSUs select vehicles within their LOS coverage as relays. As a result, the LOS coverage of those RSUs is...

Beam management is central in the operation of beamformed wireless cellular systems such as 5G New Radio (NR) networks. Focusing the energy radiated to mobile terminals (MTs) by increasing the number of beams per cell increases signal power and decreases interference, and has hence the potential to bring major improvements on area spectral efficien...

Inspired by a new feature in 5G NR called bandwidth part (BWP), this paper presents a bandwidth allocation (BA) model that allows one to adapt the bandwidth allocated to users depending on their data rate needs. Specifically, in adaptive BA, a wide bandwidth is divided into chunks of smaller bandwidths and the number of bandwidth chunks allocated t...

This paper presents a novel spatially consistent approach for modeling line-of-sight (LOS) paths in vehicular networks. We use stochastic geometry to model transmitters, obstacles, and receivers located in three parallel lines, respectively. Their geometric interactions are leveraged to characterize the existence of LOS paths. Specifically, the pro...

This paper considers the time evolution of a queue that is embedded in a Poisson point process of moving wireless interferers. The queue is driven by an external arrival process and is subject to a time-varying service process that is a function of the SINR that it sees. Static configurations of interferers result in an infinite queue workload with...

This paper concerns the performance of vehicle-to-everything (V2X) communications. More precisely, we analyze the broadcast of safety-related V2X communications in cellular networks where base stations and vehicles are assumed to share the same spectrum and vehicles broadcast their safety messages to neighboring users. We model the locations of veh...

Beam management is central in the operation of beamformed wireless cellular systems such as 5G New Radio (NR) networks. Focusing the energy radiated to mobile terminals (MTs) by increasing the number of beams per cell increases signal power and decreases interference, and has hence the potential to bring major improvements on area spectral efficien...

Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta$. The first one is the set of points that belong to some one-dimensional facet of the Voronoi tessellation and a...

This paper considers the time evolution of a queue that is embedded in a Poisson point process of moving wireless interferers. The queue is driven by an external arrival process and is subject to a time-varying service process that is a function of the SINR that it sees. Static configurations of interferers result in an infinite queue workload with...

This paper is focused on SIS epidemic dynamics (also known as the contact process) on stationary Poisson point processes of the Euclidean plane, when the infection rate of a susceptible point is proportional to the number of infected points in a ball around it. Two models are discussed, the first with a static point process, and the second where po...

Background: Haplotypes, the ordered lists of single nucleotide variations that distinguish chromosomal sequences from their homologous pairs, may reveal an individual's susceptibility to hereditary and complex diseases and affect how our bodies respond to therapeutic drugs. Reconstructing haplotypes of an individual from short sequencing reads is...

We study an N-player game where a pure action of each player is to select a non-negative function on a Polish space supporting a finite diffuse measure, subject to a finite constraint on the integral of the function. This function is used to define the intensity of a Poisson point process on the Polish space. The processes are independent over the...

We study how dense multi-antenna millimeter wave (mmWave) cellular network performance scales in terms of the base station (BS) spatial density $\lambda $ , by studying the signal-to-interference-plus-noise ratio (SINR) and the area spectral efficiency (ASE). If the number of antennas at each BS scales at least linearly with $\lambda $ , which...

Beam management is central in the operation of dense 5G cellular networks. Focusing the energy radiated to mobile terminals (MTs) by increasing the number of beams per cell increases signal power and decreases interference, and has hence the potential to bring major improvements on area spectral efficiency (ASE). This benefit, however, comes with u...

We study the problem of community detection on Euclidean random geometric graphs where each vertex has two latent variables: a binary community label and a $\mathbb{R}^d$ valued location label which forms the support of a Poisson point process of intensity $\lambda $. A random graph is then drawn with edge probabilities dependent on both the commun...

We study how dense multi-antenna millimeter wave (mmWave) cellular network performance scales in terms of the base station (BS) spatial density $\lambda$, by studying the signal-to-interference-plus-noise ratio (SINR) and the area spectral efficiency (ASE). If the number of antennas at each BS scales at least linearly with $\lambda$, which increase...

Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of i...

The primary approach to increase coverage and capacity in infrastructure-based wireless networks is densification. Densification, however, presents a major challenge when serving mobile users, which is the overhead associated with the increased rate of base station handovers. Assuming a prior knowledge of a mobile’s trajectory and base stations’ lo...

Replica-mean-field models have been proposed to decipher the activity of neural networks via a multiply-and-conquer approach. In this approach, one considers limit networks made of infinitely many replicas with the same basic neural structure as that of the network of interest, but exchanging spikes in a randomized manner. The key point is that the...

This paper concerns the performance of vehicle-to-everything (V2X) communications. More precisely, we analyze the broadcast of safety-related V2X communications in cellular networks where base stations and vehicles are assumed to share the same spectrum and vehicles broadcast their safety messages to neighboring users. We model the locations of veh...

We study the scaling laws of the signal-to-interference-plus-noise ratio (SINR) and area spectral efficiency (ASE) in multi-antenna cellular networks, where the number of antennas scales with the base station (BS) spatial density $\lambda$. We start with the MISO case having $N_t(\lambda)$ transmit antennas and a single receive antenna and prove th...

We study the scaling laws of the signal-to-interference-plus-noise ratio (SINR) and the area spectral efficiency (ASE) in multi-antenna cellular networks, where the number of antennas scales with the base station (BS) spatial density $\lambda$. We start with the MISO case with $N_t(\lambda)$ transmit antennas and a single receive antenna and prove...

This paper explores an emerging wireless Internet-of-things (IoT) architecture based on unmanned aerial vehicles (UAVs). We consider a network where a fleet of UAVs at a fixed altitude flies on planned trajectories and IoT devices on the ground are scheduled to transmit their data to the UAVs when the latter are nearby. In such a system, the UAVs’...

A stationary stochastic geometric model is proposed for analyzing the data compression method used in one-bit compressed sensing. The data set is an unconstrained stationary set, for instance all of R^n or a stationary Poisson point process in R^n. It is compressed using a stationary and isotropic Poisson hyperplane tessellation, assumed independen...

Background: Haplotypes, the ordered lists of single nucleotide variations that distinguish chromosomal sequences from their homologous pairs, may reveal an individual's susceptibility to hereditary and complex diseases and affect how our bodies respond to therapeutic drugs. Reconstructing haplotypes of an individual from short sequencing reads is a...

We characterize the stability, metastability, and the stationary regime of traffic dynamics in a single-cell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, in which users arrive as a Poisson point process in time and space, each with a file to transmit to the base station. The service rate of each user...

This paper proposes a framework to analyze a wireless architecture where vehicles collect data from devices. Roads and vehicles are modeled by a Poisson line process and a Cox point process, respectively. At any given time, each vehicle is assumed to communicate with a roadside device in a disk of radius $\nu $ centered at the vehicle, which is r...

We propose an iterated version of the Gilbert model, which results in a sequence of random mosaics of the plane. We prove that under appropriate scaling, this sequence of mosaics converges to that obtained by a classical Poisson line process with explicit cylindrical measure. Our model arises from considerations on tropical plane curves, which are...

We characterize the stability, metastability, and the stationary regime of traffic dynamics in a single-cell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, in which users arrive as a Poisson point process in time and space, each with a file to transmit to the base station. The service rate of each user...

Based on a simple object, an i.i.d. sequence of positive integer-valued random variables { a n } n ∊ℤ , we introduce and study two random structures and their connections. First, a population dynamics, in which each individual is born at time n and dies at time n + a n . This dynamics is that of a D/GI/∞ queue, with arrivals at integer times and se...

This paper explores an emerging wireless architecture based on Unmanned Aerial Vehicles (UAVs), i.e., drones. We consider a network where UAVs at fixed altitude harvest data from Internet-of-Things (IoT) devices on the ground. In such a system, the UAVs' motion activates IoT uplink transmissions and so the motion triggers the interference field and...

Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying assumptions, such as considering models in the thermodynamic mean-field limit. In the thermodynamic mean-field lim...

This paper proposes a framework to analyze an emerging wireless architecture where vehicles collect data from devices. Using stochastic geometry, the devices are modeled by a planar Poisson point process. Independently, roads and vehicles are modeled by a Poisson line process and a Cox point process, respectively. For any given time, a vehicle is a...

This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a bridge graph, generated by paths started in a fixed state at any time. The bridge graph is made into a unimodul...

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the metastability phenomenon. Large enough finite symmetric networks on regular graphs are proved to be transient for arbitrarily small inflow rates. However, the limiting non-line...

A stationary stochastic geometric model is proposed for analyzing the data compression method used in one-bit compressed sensing. The data set is an unconstrained stationary set, for instance all of $\mathbb{R}^n$ or a stationary Poisson point process in $\mathbb{R}^n$. It is compressed using a stationary and isotropic Poisson hyperplane tessellati...

We analyze a class of vector multiple access channels with additive noise, where the sum of the dimensions of the transmitted signals matches that of the received signal. We first focus on the case without power constraints, in the Poltyrev sense, using point process techniques. We find the Poltyrev capacity region for noise processes that are inde...

This paper is the third part of a series of three. The notions of unimodular discrete spaces and their unimodular (Minkowski and Hausdorff) dimensions were introduced in Part I. The connections of these dimensions to the growth rate were discussed in Part II. In this paper, complements to the mathematical framework of unimodular dimensions (packing...

The notions of unimodular Minkowski and Hausdorff dimensions are defined in [F. Baccelli, M.-O. Haji-Mirsadeghi, A. Khezeli, preprint (2018)] for unimodular random discrete metric spaces. The present paper is focused on the connections between these notions and the polynomial growth rate of the underlying space. It is shown that bounding the dimens...

This work introduces two new notions of dimension, namely the unimodular Minkowski and Hausdorff dimensions, which are inspired from the classical analogous notions. These dimensions are defined for unimodular discrete spaces, introduced in this work, which provide a common generalization to stationary point processes under their Palm version and u...

Disruptive changes are underway in the automotive industry as large-scale platforms based on vehicular fleets are deployed to deliver ride sharing and delivery services. Such platforms can also be leveraged to deliver wireless connectivity services, e.g., large-scale connectivity for the Internet of Things (IoT). This paper examines a network archi...

Based on a simple object, an i.i.d. sequence of positive integer-valued random variables, $\{a_n\}_{n\in \mathbb{Z}}$, we introduce and study two random structures and their connections. First, a population dynamics, in which each individual is born at time $n$ and dies at time $n+a_n$. This dynamics is that of a D/GI/$\infty$ queue, with arrivals...

This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads. We d...

This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads. We d...

This paper is centered on covariant dynamics on unimodular random graphs and random networks (marked graphs), namely maps from the set of vertices to itself which are preserved by graph or network isomorphisms. Such dynamics are referred to as vertex-shifts here. The first result of the paper is a classification of vertex-shifts on unimodular rando...

This paper studies the asymptotic properties of area spectral efficiency (ASE) of a downlink cellular network in the limit of very dense base station (BS) and user densities. This asymptotic analysis relies on three assumptions: (1) interference is treated as noise; (2) the BS locations are drawn from a Poisson point process; (3) the path loss func...

This paper studies the asymptotic properties of average area spectral efficiency (ASE) of a downlink cellular network in the limit of very dense base station (BS) and user densities. This asymptotic analysis relies on three assumptions: (1) interference is treated as noise; (2) the BS locations are drawn from a Poisson point process; (3) the path l...