arXiv subjects

François Baccelli

Publications and source records attributed to François Baccelli.

At least 19 recordsLinked to original sources

arXiv2026

On the Lack of Periodicity of Walker Satellite Constellation Routing Tables

In a referential that rotates with Earth, the dynamics of the configurations of satellites in a Delta Walker constellation can be analyzed as a dynamical system as a function of a translation on the torus. This paper extends this type of analysis to routing over a Walker constellation, leveraging fixed ground relays. It considers any deterministic, time-invariant routing rule on such a collection of satellites and relays. The main object of interest is the routing table associated with this rule, which specifies, for all source-destination pairs, a route made of satellites and relays between them, for instance the shortest, together with angular information on next hop at each step of the route, which is essential for beamforming in this context. The main result is that, for each such routing rule, the routing table inherits the dichotomy of the torus flow: when the ratio of the Earth-spin and satellite angular speeds is rational, the routing table process is periodic with the same period as the constellation. When it is irrational, the table is non periodic but admits ergodic long-run averages which can be computed as ensemble averages w.r.t. an explicit invariant measure. Simulations with mixed satellite--gateway greedy routing illustrate these findings in terms of both temporal and spectral properties of the Walker routing table time series. The paper also discusses how to define metrics that cope with such non periodic fluctuations when present. This is illustrated by a comparison of the round-trip times between two far away cities as offered by a Walker constellation using greedy routing on one side, and by the currently available terrestrial fiber on the other side. It is shown how ergodicity can be used to make this comparison between the time varying instantaneous round trip times of the constellation and the constant round trip time of the fiber network meaningful.

cs.IT↗

arXiv2026

Decoding Delay Guarantees of Space Regulated Multiple Access Random Wireless Networks using Successive Interference Cancellation

This paper is focused on decoding delay guarantees in wireless networks, where messages have a given signal-to-interference-plus-noise ratio threshold $η_0$ to meet in order to be successfully decoded, and where transmissions should occur within some strict time constraints. Its main contribution consists in quantifying the worst-case transmissions decoding delays in the uplink of cellular and cell-free networks using successive interference cancellation. We show how such decoding delay guarantees can be obtained using spatial network calculus, a new tool introduced recently, and in particular spatial regulation. The results rely on the assumption of absence of fading. We nevertheless outline what this approach will lead to in the fading case for cellular networks.

cs.NI↗

arXiv2026

On a Class of Dynamical Poisson-Voronoi Tessellations

Consider a dynamical network model featuring mobile stations on the Euclidean plane. The initial locations of the stations are given by a homogeneous Poisson point process. The stations are all moving at a constant speed and in a random direction. Consider fixed users located in the Euclidean plane, which are served by the mobile stations. Each user stays connected to the nearest station at any given point of time. Since the stations are moving, a user disconnects and connects with different stations over time, by always selecting which ever station is the closest. This gives rise to a dynamical version of the Poisson-Voronoi tessellation. The focus of this paper is on the sequence of ``handover'' events of a typical user, which are the epochs when its association changes. This defines a point process on the time-axis, the ``handover point process''. We show that this point process is stationary and we determine its main properties, in particular its intensity and the joint distribution of its inter-event times. We also analyze the handover Palm distributions of several variables of practical interest. This includes the distance to the closest mobile stations and the point process of all other mobile stations at handover epochs. The analysis is conducted both in the single-speed and in the multi-speed scenarios. Closed form expressions are obtained in both cases. It leads to the identification of the three dimensional state variables that ``Markovize'' the association dynamics. The analysis is based on a specific system of non-compact particles. The motivations are in the modeling of low or medium orbit satellite wireless communication networks. The model studied here is a planar ``caricature'' of this problem, which is initially defined on the sphere.

math.PR↗

arXiv2026

Interference Queueing Networks: A Replica Mean-Field Approach in the Symmetric Setting

We propose a model for evaluating the performance of wireless communication networks beyond the ubiquitous full-buffer assumption, under which every transmitter is always active. The network is represented by N interacting queues arranged on a torus, with homogeneous arrival rate and service rates depending on the activity of neighboring interferers. More precisely, each queue is associated with a transmitter-receiver pair, and its service rate is given by the Shannon capacity, which depends on the corresponding Signal-to-Interference-plus-Noise Ratio (SINR). Since interfering transmitters only emit when their queue is non-empty, the SINR, and hence the service rate, improves when neighboring queues are empty. We first derive the stability region of the system. To investigate the stationary regime, we introduce two mean-field approximations. The first one is obtained from a finite K-replica system, for which we prove propagation of chaos as K goes to infinity. The second one describes a queueing system evolving in a suitably chosen autonomous environment. We derive quantitative estimates comparing these two approximations. Finally, we prove that the original interacting queueing system converges exponentially fast to stationarity.

math.PR↗

arXiv2026

Densification Converses for Walker Constellations

We establish densification converses for Walker LEO constellations under nearest-visible association in the full-frequency-reuse setting. Performance is evaluated under the invariant (stationary) measure induced by the constellation/Earth dynamics on the user--constellation ``phase state.'' A key Walker-specific feature, absent from unbounded planar models, is that association is restricted to a bounded visible cap determined by Earth geometry. Under power-law path-loss, a two-level antenna-gain model, i.i.d.\ nonnegative fading with unit mean and finite second moment, and nonzero noise, we prove that increasing the total satellite count $N=N_oN_s$ forces the aggregate interference to grow at least linearly in $N$, while the useful signal remains uniformly bounded above. Consequently, the downlink SINR coverage probability at any fixed threshold and the ergodic spectral efficiency both vanish as $N\to\infty$. These collapse statements concern link-level performance on one shared time--frequency resource block and do not imply that the aggregate capacity of the overall multi-resource network vanishes. The key technical ingredient is a deterministic visibility-annulus block lemma, uniform over all sufficiently large constellations and all ``phase states,'' showing that a fixed fraction of visible satellites lies in a distance annulus strictly inside the horizon; this yields explicit finite-$N$ collapse bounds. In particular, we derive nonasymptotic $O(1/N)$ upper bounds on both coverage and ergodic spectral efficiency. Finally, in the case of frequency reuse through independent thinning, with activity probability $q$, we show that avoiding densification collapse necessarily requires $qN=O(1)$, equivalently a reuse factor $Ω(N)$, and we obtain a corresponding explicit $O(1/(qN))$ upper bound.

cs.IT↗

arXiv2026

Seasonal Statistics of Shannon Rate in a Dynamical Poisson-Voronoi Cellular Network

In this work we consider a dynamical cellular communication network in which mobile base stations (BSs) are modeled as a homogeneous Poisson point process on $\mathbb{R}^2$. Each base station moves at a constant speed in a random direction. A typical user connects to the nearest base station and it experiences variable signal and interference powers depending on the distance of all the stations. Along the motion of the stations, the user swaps its serving station, and such an event is called a {\em handover}. We are interested in the performance evaluation of the system under some classical and tropical metrics of interest at different time of events, inducing handovers, maximal proximity of serving station, nearest interferer at closest or farthest distance with respect to the user or at any typical time epoch. The main results of the paper are closed or integral form expressions for the basic metrics of interest, in particular coverage probability and Shannon rate at these epochs. We can make an analogy with ``seasons'' based on the fluctuations of signal and interference power. Strong or mild signal or interference power correspond to different seasons of Shannon rate along the evolution of the system. We also provide a complete comparison study of the metrics at interest at these epochs.

math.PR↗

arXiv2026

Unified Evaluation Methodology for AI-Native Integrated Sensing and Communication

Integrated Sensing and Communication (ISAC) couples radio sensing, data transmission, and control actions within a single closed-loop system. When Artificial Intelligence (AI)-driven policies adapt sensing and communication online across a variety of sensing tasks and objectives, end-to-end performance is shaped not only by waveform and channel conditions but also by inference latency, uncertainty, environmental dynamics, and hardware non-idealities, leading to fundamental trade-offs between sensing accuracy, communication reliability, and resource overhead. This manuscript presents a unified system architecture and evaluation methodology for AI-native ISAC, defined as ISAC in which learning-based agents adapt sensing, communication, and actuation policies online under uncertainty. We formalize the design space of closed-loop ISAC, propose a three-stage validation pipeline from bounds and feasibility analysis, through high-fidelity digital-twin simulation, to preliminary over-the-air validation, and provide a minimal reporting checklist that links technical Key Performance Indicators (KPIs) (e.g., data rate, SINR, target detection, parameter estimation, track quality, localization error, outage, latency, overhead, and energy per decision) to application-level Key Value Indicators (KVIs) (e.g., availability and mission effectiveness). Two representative instantiations, specifically Unmanned Aerial Vehicle (UAV)-based outdoor and Reconfigurable Intelligent Surface (RIS)-enabled indoor coverage extensions, are used to illustrate how to structure reproducible baselines and comparable evidence across heterogeneous deployments, helping bridge the gap between theoretical ISAC gains and deployment-ready performance claims.

cs.NI↗

arXiv2026

Hierarchical Clustering Algorithms on Poisson and Other Stationary Point Processes

This paper introduces a hierarchical clustering algorithm, the Clustroid Hierarchical Nearest Neighbor ($\mathrm{CHN}^2$), designed for datasets with a countably infinite number of data represented by points in the Euclidean space. The method builds clusters across successive levels by linking nearest-neighbor points or clusters using the clustroid distance. The properties of this algorithm make it suitable for very large datasets. To evaluate its properties, we first apply the algorithm to the homogeneous Poisson point process, which serves as a natural null-hypothesis model with no intrinsic data aggregation. In this setting, the algorithm generates a random forest that is a deterministic factor of the Poisson point process, and hence unimodular. We prove that at every level, the level-$k$ graph has only finite connected components (a.s.) and derive bounds on their mean size. We also establish the existence of a limiting graph as the number of levels tends to infinity. In this limit, clusters are shown to be all infinite and one-ended, which induces a natural order within each component and supports a tree-like phylogenetic interpretation. Beyond the Poisson case, we extend the analysis to a class of Cox and more general stationary point processes without second-order descending chains (introduced here), for which analogous results hold. Simulations show that comparing the Cox case with the Poisson baseline allows an efficient detection of aggregation, thereby linking the stochastic-geometric analysis to practical clustering tasks.

math.PR↗

arXiv2026

The Relay Random Tree: A Stochastic Geometry Approach of Multihop Relay in an Urban Visibility Setting

In a recent work (Lee, Baccelli $'25$), a one dimensional stochastic geometry model was introduced to study Line of Sight (LoS) connections using Reconfigurable Intelligent Surfaces (RIS), in the context of non terrestrial networks. In this model, signal can be propagated in a urban environment, with buildings acting as obstacles with RIS (which, for the scope of this present article can essentially be thought of as relays) on their rooftops, relaying the connection. The present paper extends this model by both allowing arbitrary distributions for the buildings heights, and considering multi-hop connections. Those generalities also lead to considering structural problems linked to the total load of a relay. Furthermore, studying this Line of Sight connection geometry at the light of geometric random graph theory, we show that it constitutes a computationally well understood example that highlights the different classes of the Eternal Family Trees (EFTs) classification.

math.PR↗

arXiv2026

Poisson Hail on a Wireless Ground

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 directly accessing the shared resources upon arrival, a customer is considerate and waits to access them until nearby users in service have left. This new model can be seen as a missing piece of a larger puzzle that contains such dynamics as spatial birth-and-death processes, the Poisson-Hail model, and wireless dynamics as key other pieces. It is shown that, under natural assumptions, this model can be represented as a Markov process on the space of counting measures. The main results are then two-fold. The first is on the shape of the stability region and, more precisely, on the characterization of the critical value of the arrival rate that separates stability from instability. The second is of a more qualitative or perhaps even ethical nature. There is evidence that for natural values of the system parameters, the implementation of sensing and collision avoidance stabilizes a system that would be unstable if immediate access to the shared resources would be granted. In other words, for these parameters, renouncing greedy access makes sharing sustainable, whereas indulging in greedy access kills the system.

cs.IT↗

arXiv2026

The Skyline Process: Quantifying Sky Visibility in 3D Urban Environments

Non-terrestrial networks (NTNs) are considered a promising technology for seamless, universal communication in the 6G era. However, signals from NTN elements to ground users are often blocked by high-rise buildings in dense urban environments. To quantify this blocking effect, in this paper, we propose a novel analytical framework by modeling the location of buildings as a 3D skyline process based on stochastic geometry and we derive closed-form expressions for the distribution of the blockage elevation angles. Furthermore, we extend our analysis to include spatially correlated blockage effects and analyze the spectral properties of the Skyline process using power spectral density (PSD) and autocorrelation function (ACF). Based on these theoretical findings, we present numerical results that provide insights into the design of LEO satellite networks by computing the mean number of visible satellites and the outage probability. We provide a decorrelation angle that serves as a useful threshold for obtaining the satellite diversity gain. These findings provide first analytical steps toward designing and user connection strategies to NTNs in urban environments.

math.PR↗

arXiv2026

Performance Guarantees of Cellular Networks with Hardcore Regulation and Scheduling

Providing performance guarantees is one of the critical objectives of recent and future communication networks, toward which regulations, i.e., constraints on key system parameters, have played an indispensable role. This is the case for large wireless communication networks, where spatial regulations (e.g., constraints on intercell distance) have recently been shown, through a spatial network calculus, to be essential for establishing provable wireless link-level guarantees. In this work, we focus on performance guarantees for the downlink of cellular networks where we impose a hardcore (spatial) regulation on base station (BS) locations and evaluate how BS scheduling (which controls which BSs can transmit at a given time) impacts performance. Hardcore regulation is the simplest form of spatial regulation that enforces a minimal distance between any pair of transmitters in the network. Within this framework of spatial network calculus, we first provide an upper bound on the power of total interference for a spatially regulated cellular network, and then, identify the regimes where scheduling BSs yields better link-level rate guarantees compared to scenarios where base stations are always active. The hexagonal cellular network is analyzed as a special case. The results offer insights into what spatial regulations are needed, when to choose scheduling, and how to potentially reduce the network power consumption to provide a certain target performance guarantee.

cs.IT↗

arXiv2025

Spherical Point Process with Random Heights: New Approach for Modeling and Analysis of Downlink Satellite Networks

The Low Earth Orbit (LEO) satellite industry is undergoing rapid expansion, with operators competitively launching satellites due to the first-come, first-served principle governing orbital rights. This has led to the formation of increasingly large-scale, volumetric constellation where satellites operate across a diverse range of altitudes. To address the need for analyzing such complex networks, this paper establishes a new analytical framework for LEO constellations by leveraging a 3D Poisson point process (PPP). Specifically, we introduce a random height model (RHM) that can capture various altitude distributions by applying a random radial displacement to points generated by a homogeneous PPP on a nominal shell. Building on this, we derive an analytical expression for the downlink coverage probability. To motivate our model, we show that the altitude distributions of several leading satellite constellations, including Starlink, align with our model's assumptions. We then demonstrate through Monte Carlo simulations that the coverage probability of our RHM closely matches that of these real-world networks. Finally, we confirm the accuracy of our analytical expressions by showing their agreement with simulation results. Our work thereby provides a powerful tool for understanding and predict how the statistical distribution of satellite altitudes impacts network performance.

cs.IT↗

arXiv2024

A Novel Analytical Model for LEO and MEO Satellite Networks based on Cox Point Processes

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 incorporate this geometric property of LEO or MEO satellite constellations by developing a Cox point process model that jointly produces orbits and satellites on these orbits. Our work contrasts with previous modeling studies that presumed satellite locations to be entirely random, thereby overlooking the fundamental fact that satellites are jointly positioned on orbits. Employing this Cox model, we analyze the network performance experienced by users located on Earth. Specifically, we evaluate the no-satellite probability of the proposed network and the Laplace transform of the interference created by such a network. Using it, we compute its SIR (signal-to-interference) distribution, namely its coverage probability. By presenting fundamental network performance as functions of key parameters, this model allows one to assess the statistical properties of downlink LEO or MEO satellite communications and can thus be used as a system-level design tool to operate and optimize forthcoming complex LEO or MEO satellite networks.

eess.SP↗

arXiv2024

Cox Point Processes for Multi Altitude LEO Satellite Networks

To model existing or future low Earth orbit (LEO) satellite networks leveraging multiple constellations, we propose a simple analytical approach to represent the clustering of satellites on orbits. More precisely, we develop a variable-altitude Poisson orbit process that effectively captures the geometric fact that satellites are always positioned on orbits, and these orbits may vary in altitude. Conditionally on the orbit process, satellites situated on these orbits are modeled as linear Poisson point processes, thereby forming a Cox point process. For this model, we derive useful statistics, including the distribution of the distance from the typical user to its nearest visible satellite, the outage probability, the Laplace functional of the proposed Cox satellite point process, and the Laplace transform of the interference power from the Cox-distributed satellites under general fading. The derived statistics enable the evaluation of the performance of such LEO satellite communication systems as functions of network parameters.

eess.SP↗

arXiv2024

Genealogies of records of stochastic processes with stationary increments as unimodular trees

Consider a stationary sequence $X=(X_n)$ of integer-valued random variables with mean $m \in [-\infty, \infty]$. Let $S=(S_n)$ be the stochastic process with increments $X$ and such that $S_0=0$. For each time $i$, draw an edge from $(i,S_i)$ to $(j,S_j)$, where $j>i$ is the smallest integer such that $S_j \geq S_i$, if such a $j$ exists. This defines the record graph of $X$. It is shown that if $X$ is ergodic, then its record graph exhibits the following phase transitions when $m$ ranges from $-\infty$ to $\infty$. For $m<0$, the record graph has infinitely many connected components which are all finite trees. At $m=0$, it is either a one-ended tree or a two-ended tree. For $m>0$, it is a two-ended tree. The distribution of the component of $0$ in the record graph is analyzed when $X$ is an i.i.d. sequence of random variables whose common distribution is supported on $\{-1,0,1,\ldots\}$, making $S$ a skip-free to the left random walk. For this random walk, if $m<0$, then the component of $0$ is a unimodular typically re-rooted Galton-Watson Tree. If $m=0$, then the record graph rooted at $0$ is a one-ended unimodular random tree, specifically, it is a unimodular Eternal Galton-Watson Tree. If $m>0$, then the record graph rooted at $0$ is a unimodularised bi-variate Eternal Kesten Tree. A unimodular random directed tree is said to be record representable if it is the component of $0$ in the record graph of some stationary sequence. It is shown that every infinite unimodular ordered directed tree with a unique succession line is record representable. In particular, every one-ended unimodular ordered directed tree has a unique succession line and is thus record representable.

math.PR↗

arXiv2024

Analysis of a Spatially Correlated Vehicular Network Assisted by Cox-distributed Vehicle Relays

In vehicle-to-all (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 geometry to model and analyze a spatially correlated heterogeneous vehicular network where both RSUs and vehicular relays serve network users such as pedestrians or other vehicles. We present an analytical model where the spatial correlation between roads, RSUs, relays, and users is systematically modeled via Cox point processes. Assuming users are associated with either RSUs or relays, we derive the association probability and the coverage probability of the typical user. Then, we derive the user throughput by considering interactions of links unique to the proposed network. This paper gives practical insights into designing spatially correlated vehicular networks assisted by vehicle relays. For instance, we express the network performance such as the user association, SIR coverage probability, and the network throughput as the functions of network key geometric variables. In practice, this helps one to optimize the network so as to achieve ultra reliability or maximum user throughput of a spatially correlated vehicular networks by varying key aspects such as the relay density or the bandwidth for relays.

eess.SP↗

arXiv2023

Spatial Network Calculus and Performance Guarantees in Wireless Networks

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 classical network calculus. Specifically, two classes of regulations are defined: one includes ball regulation and shot-noise regulation, which are shown to be equivalent and upper constraint interference; the other one includes void regulation, which lower constraints the signal power. These regulations are defined both in the strong and weak sense: the former requires the regulations to hold everywhere in space, whereas the latter only requires the regulations to hold as observed by a jointly stationary point process. Using this approach, we derive performance guarantees in device-to-device, ad hoc, and cellular networks under proper regulations. We give universal bounds on the SINR for all links, which gives link service guarantees based on information-theoretic achievability. They are combined with classical network calculus to provide end-to-end latency guarantees for all packets in wireless queuing networks. Such guarantees do not exist in networks that are not spatially regulated, e.g., Poisson networks.

cs.IT↗