arXiv subjects

Francois Baccelli

Publications and source records attributed to Francois Baccelli.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical System Characterization of Heterogeneous Walker Satellite Networks: An Orbit-Aware Stochastic Geometry Perspective

Heterogeneous and in particular multi-altitude low Earth orbit (LEO) satellite constellations exhibit complex spatial and temporal structures, which require new modeling tools for their performance analysis. In this paper, we develop an orbit-aware stochastic geometry framework modeling today's LEO satellites on various orbits and various altitudes. In particular, we characterize such a system as the superposition of multiple Walker point processes and formulate it as a dynamical system determined by an initial condition and the rotation speeds of satellites and Earth. We show that when the speeds are rationally commensurable, the proposed satellite system is periodic. Then, we show that the system is ergodic when the speeds are rationally independent, establishing a theoretical link between time averages of the system and the expectation of it under the invariant measure. We derive the nearest-satellite distance distribution of a typical receiver at a given latitude and analyze the signal to interference-plus-noise ratio (SINR) coverage probability of the typical receiver. We then derive the ergodic throughput of the downlink communication to the typical receiver. Overall, the proposed framework offers a rigorous and tractable tool for analyzing downlink performance in Walker-type heterogeneous LEO satellite networks.

cs.IT↗

arXiv2026

Joint Visibility Analysis of RIS in Non-Terrestrial Networks through Stochastic Geometry

Non-Terrestrial networks (NTNs) are a key theme in upcoming 6G communications, especially for ubiquitous coverage. Urban environments, comprising of high rise buildings often result in blocking the line of sight (LoS) path between the user equipment (UE) and the NTN base station (NTN-BS). In this paper we investigate the situation where reconfigurable intelligent surfaces (RIS) are deployed on the building roof-tops to ensure multi-hop connectivity between the UE and the NTN-BS. In such a scenario, it becomes crucial to statistically study the LoS visibility of the RIS from the UE as well as from the NTN-BS, hence termed as joint visibility. In this work, accounting for the dual stochasticity arising from the locations of the RIS deployed buildings and the respective random building heights, we statistically study the probability of joint RIS visibility in a two-dimensional (2D) scenario considering a deterministic location of the NTN-BS. Further, we study the joint RIS visibility statistics conditional on the UE-NTN link being LoS or non-LoS. For the RISs deployed as a point point process (PPP) having exponentially distributed heights, the expected RISs jointly visible under the unconditional and conditional geometric settings are derived in closed form. Interestingly, in the 2D setting, the maximum expected RISs jointly visible, unconditionally, is twice the Basel number $(\pi^2/ 6)$. The simulated results are analyzed over building density, average building height, the altitude and position of the NTN-BS. We also illustrate probability heatmaps, demonstrating the strongest chance to have a RIS used conditioned on the system geometry. This study is expected to be useful in planning the deployment of RIS in urban areas, improving the signal and for assessing economic aspects.

eess.SY↗

arXiv2026

Indistinguishability in One-or-Two-Ended Forests on Unimodular Random Graphs

Indistinguishability is a form of ergodicity, introduced by Lyons and Schramm for percolation clusters, that has become a fundamental notion in the theory of random infinite graphs. We prove the indistinguishability of connected components for a broad family of random one-ended or two-ended oriented forests on unimodular graphs using a new approach. We unify these models by introducing `coalescing Markov trajectories' (CMTs), which encompass a wide range of classical coalescing models, including river models and coalescing random walks. We also establish the indistinguishability of level-sets, a problem that has not previously been studied and lies beyond the scope of existing techniques. Using the latter, we prove that the clusters of the stationary voter model on a unimodular graph are indistinguishable. The core of the proof approach is the reduction of the indistinguishability of the components (respectively, level-sets) to the ergodicity (respectively, tail triviality) of the ancestry chain of the root. This shows a structural property that the ancestry chain is the fundamental object governing indistinguishability. For CMTs, the proof is completed by proving the tail triviality of Markov chains on unimodular random graphs, which is of independent interest. The flexibility of the approach is illustrated by further applications: It yields indistinguishability results for some point-map models on Bernoulli and Poisson point processes, including Howard's model and the strip point-map. It also yields a new and substantially simpler proof of indistinguishability for the wired uniform spanning forest, which is the only one-ended model for which indistinguishability was previously studied in the literature.

math.PR↗

arXiv2026

The Multiserver-Job Stochastic Recurrence Equation for Cloud Computing Performance Evaluation

We study the Multiserver-Job Queuing Model (MJQM) with general independent arrivals and service times under FCFS scheduling, using stochastic recurrence equations (SREs) and ergodic theory. We prove the monotonicity and separability properties of the MJQM SRE, enabling the application of the monotone-separable extension of Loynes' theorem and the formal definition of the MJQM stability condition. Based on these results, we introduce and implement two algorithms: one for drawing sub-perfect samples (SPS) of the system's workload and the second one to estimate the system's stability condition given the statistics of the jobs' input stream. The SPS algorithm allows for a massive GPU parallelization, greatly improving the efficiency of performance metrics evaluation. We also show that this approach extends to more complex systems, including MJQMs with typed resources.

cs.PF↗

arXiv2025

Closed-form analysis of Multi-RIS Reflected Signals in RIS-Aided Networks Using Stochastic Geometry

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 aggregated reflections from multiple RISs using the Laplace transform, we analytically assess the performance impact of RIS-reflected signals by integrating this characterization into well-established stochastic geometry frameworks. Specifically, we derive closed-form expressions for the Laplace transform of the reflected signal power in several deployment scenarios. These analytical results facilitate performance evaluation of RIS-enabled enhancements. Numerical simulations validate that optimal RIS placement favors proximity to BSs or user equipment (UEs), and further quantify the impact of reflected interference, various fading assumptions, and diverse spatial deployment strategies. Importantly, our analytical approach shows superior computational efficiency compared to Monte Carlo simulations.

cs.PF↗

arXiv2025

Subthreshold moment analysis of neuronal populations driven by synchronous synaptic inputs

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 magnitude of membrane voltage fluctuations. We found that accounting for these fluctuations requires weak but nonzero synchrony in the spiking activity, in amount that are consistent with experimentally measured spiking correlations. Here we investigate whether such synchrony can explain additional statistical features of the measured neural activity, including neuronal voltage covariability and voltage skewness. Addressing this question involves conducting a generalized moment analysis of conductance-based neurons in response to input drives modeled as correlated jump processes. Technically, we perform such an analysis using fixed-point techniques from queuing theory that are applicable in the stationary regime of activity. We found that weak but nonzero synchrony can consistently explain the experimentally reported voltage covariance and skewness. This confirms the role of synchrony as a primary driver of cortical variability and supports that physiological neural activity emerges as a population-level phenomenon, especially in the spontaneous regime.

q-bio.NC↗

arXiv2025

A Stochastic Geometry Based Techno-Economic Analysis of RIS-Assisted Cellular Networks

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 relative cost model that considers the total cost of ownership (TCO) of deploying additional nodes, either BSs or RISs. We assume a return on investment (RoI) that is proportional to the system's spectral efficiency. The latter is evaluated based on a stochastic geometry model that gives an integral formula for the ergodic rate in cellular networks equipped with RISs. The marginal RoI for any investment strategy is determined by the partial derivative of this integral expression with respect to node densities. We investigate two case studies: throughput enhancement and coverage hole mitigation. These examples demonstrate how operators could determine the optimal investment strategy in scenarios defined by the current densities of BSs and RISs, and their relative costs. Numerical results illustrate the evolution of ergodic rates based on the proposed investment strategy, demonstrating the investment decision-making process while considering technological and economic factors. This work quantitatively demonstrates that strategically investing in RISs can offer better system-level benefits than solely investing in BS densification.

cs.PF↗

arXiv2024

Stochastic Geometry and Dynamical System Analysis of Walker Satellite Constellations

In practice, low Earth orbit (LEO) and medium Earth orbit (MEO) satellite networks consist of multiple orbits which are populated with many satellites. A widely used spatial architecture for LEO or MEO satellites is the Walker constellation, where the longitudes of orbits are evenly spaced and the satellites are equally spaced along the orbits. In this paper, we develop a stochastic geometry model for the Walker constellations. This proposed model enables an analysis based on dynamical system theory, which allows one to address essential structural properties such as periodicity and ergodicity. It also enables a stochastic geometry analysis under which we derive the performance of downlink communications of a typical user at a given latitude, as a function of the key constellation parameters.

cs.IT↗

arXiv2024

How Much Can Reconfigurable Intelligent Surfaces Augment Sky Visibility: A Stochastic Geometry Approach

This paper uses the theory of point processes and stochastic geometry to quantify the sky visibility experienced by users located in an urban 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 process framework is first used to characterize the distribution of the blockage angle, which limits the visibility of a typical user into the sky due to the obstruction by buildings. In the context of communications, this distribution is useful when users try to connect to the nodes of an aerial or non-terrestrial network in a Line-of-Sight way. Within this context, the point process framework can also be used to investigate the gain of connectivity obtained thanks to Reconfigurable Intelligent Surfaces. Assuming that such surfaces are installed on the top of buildings to extend the user's sky visibility, this point process approach allows one to quantify the gain in visibility and hence the gain in connectivity obtained by the typical user. The distributional properties of visibility-related metrics are cross-validated by comparison to simulation results.

math.PR↗

arXiv2023

A Stochastic Geometry Framework for Performance Analysis of RIS-assisted OFDM Cellular Networks

The reconfigurable intelligent surface (RIS) technology allows one to engineer spatial diversity in complex cellular networks. This paper provides a framework for the system-level performance assessment of RIS-assisted networks and in particular downlink coverage probability and ergodic rate. To account for the inherent randomness in the spatial deployments of base stations (BSs) and RISs, we model the placements of the RISs as point processes (PPs) conditioned on the associated BSs, which are modeled by a Poisson point process (PPP). These RIS PPs can be adapted based on the deployment strategy. We focus on modeling the RISs as a Mat\'ern cluster process (MCP), where each RIS cluster is a finite PPP with support a disc centered on the association BS. We assume that the system uses the orthogonal frequency division multiplexing (OFDM) technique to exploit the multipath diversity provided by RISs. The coverage probability and the ergodic rate can be evaluated when RISs operate as batched powerless beamformers. The resulting analytical expressions provide a general methodology to evaluate the impact of key RIS-related parameters, such as the batch size and the density of RISs, on system-level performance. To demonstrate the framework's broad applicability, we also analyze a RIS placement variant where RISs are deployed around coverage holes. Numerical evaluations of the analytical expressions and Monte-Carlo simulations jointly validate the proposed analytical approach and provide valuable insights into the design of future RIS-assisted cellular networks.

cs.IT↗

arXiv2023

On the Poisson Follower Model

We introduce a stochastic geometry dynamics inspired by opinion dynamics that captures the essence of modern asymmetric social networks with leaders and followers. Points in the Euclidean space represent opinions, and the leader of an agent is the one with the closest opinion. In this dynamics, each follower updates its opinion by halving the distance to its leader. We demonstrate that this simple dynamics and its iterations exhibit several interesting purely geometric phenomena related to the evolution of leadership and opinion clusters, which resemble those observed in social networks. We also show that when the initial opinions are randomly distributed as a stationary Poisson point process, the spatial frequency of each of these phenomena can be expressed through an integral geometry formula involving semi-algebraic domains. Finally, we analyze numerically the limiting behavior of this follower dynamics. In the Poisson case, the agents fall into two categories: ultimate followers, who continue updating their opinions indefinitely, and ultimate leaders, who adopt a fixed opinion after a finite time. Spatial discrete event simulations support all our findings.

math.PR↗

arXiv2022

Migration-Contagion Processes

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 either I for infected, or S for susceptible. They can swap their state either from I to S or from S to I only in stations. At any station, each S customer becomes I with rate alpha Y if there are Y infected customers in the station, and each I customer recovers and becomes S with rate beta. We let N tend to infinity and assume that lim_{N\to infty} K_N/N= eta>0. The main problem is about the set of parameters for which there exists a stationary regime where the epidemic survives in the thermodynamic limit. We establish several structural properties of the system, which allow us to give the phase transition diagram of this thermodynamic limit w.r.t. eta. The analysis of the SIS model reduces to that of a wave-type PDE for which we found no explicit solution. This SIS model is one among several companion stochastic processes with migration and contagion. Two of them are discussed as they provide some bounds and approximations to SIS. These two variants are the DOCS (Departure On Change of State) and the AIR (Averaged Infection Rate), which both admit closed-form solutions. The AIR system is a mean-field model where the infection mechanism is based on the empirical average of the number of infected customers in all stations. The latter admits a product-form solution. DOCS features accelerated migration in that each change of SIS state implies an immediate departure. It leads to another wave-type PDE that admits a closed-form solution.

math.PR↗

arXiv2021

Bandwidth Allocation and Service Differentiation in D2D Wireless Networks

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 to a user depends on its needs or type. Although BWP in 5G NR mandates allocation of a set of contiguous bandwidth chunks, our BA model also allows other assumptions on chunk allocation such as the allocation of any set of bandwidth chunks, as in, e.g., LTE resource allocation, where chunks are selected uniformly at random. The BA model studied here is probabilistic in that the user locations are assumed to form a realization of a Poisson point process and each user decides independently to be of a certain type with some probability. This model allows one to quantify spectrum sharing and service differentiation in this context, namely to predict what performance a user gets depending on its type as well as the overall performance. This is based on exact representations of key performance metrics for each user type, namely its success probability, the meta distribution of its signal-to-interference ratio, and its Shannon throughput. We show that, surprisingly, the higher traffic variability stemming from adaptive BA is beneficial: when comparing two networks using adaptive BA and having the same mean signal and the same mean interference powers, the network with higher traffic variability performs better for all these performance metrics. With respect to Shannon throughput, we observe that our BA model is roughly egalitarian per Hertz and leads to a linear service differentiation in aggregated throughput value.

cs.IT↗

arXiv2020

Stability and Metastability of Traffic Dynamics in Uplink Random Access Networks

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 is based on its signal to interference plus noise ratio, where the interference is from other active users in the cell. Once the file is fully transmitted, the user leaves the cell. We derive the necessary and sufficient condition for network stability, which is independent of the specific bounded path loss function. A novel observation is that for a certain range of arrival rates, the network appears stable for a possibly long time, and then suddenly exhibits instability. This property, which is known in statistical physics but rarely observed in wireless communication, is called metastability. Finally, we propose two heuristic characterizations based on mean-field interpretation, of the network steady-state regime when it exists. The first-order approximation is very simple to compute, but loose in some regimes, whereas the second-order approximation is more sophisticated but tight for the whole range of arrival rates.

cs.IT↗

arXiv2020

Nash equilibrium structure of Cox process Hotelling games

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 players, and the value to a player is the measure of the union of its open Voronoi cells in the superposition point process. Under randomized strategies, the process of points of a player is thus a Cox process, and the nature of competition between the players is akin to that in Hotelling competition games. We characterize when such a game admits Nash equilibria and prove that when a Nash equilibrium exists, it is unique and comprised of pure strategies that are proportional in the same proportions as the total intensities. We give examples of such games where Nash equilibria do not exist. A better understanding of the criterion for the existence of Nash equilibria remains an intriguing open problem.

math.PR↗

arXiv2020

Escaping the Densification Plateau in Cellular Networks Through mmWave Beamforming

We study how dense multi-antenna millimeter wave (mmWave) cellular network performance scales in terms of the base station (BS) spatial density $λ$, 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 $λ$, which increases the number of possible beam configurations and their main-lobe gain, and decreases their side-lobe gain, we prove that the SINR approaches a finite random variable that is independent of $λ$ and the ASE scales at least linearly with $λ$. In contrast, if the number of antennas scales sub-linearly with $λ$, then the SINR decays to zero and the ASE saturates to a constant. Thus, by moving to higher carrier frequencies with successively smaller antennas, and exploiting the correspondingly increased directionality, cellular operators can in principle avoid the densification plateau (or collapse) in cellular networks and instead continue to harvest linear sum throughput gains through BS densification.

cs.IT↗

arXiv2020

Modeling and Analysis of Data Harvesting Architecture based on Unmanned Aerial Vehicles

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' motion triggers the uplink transmissions of the IoT devices. As a result, network performance is determined by the geometric and dynamic characteristics of the system. We propose a joint stationary model for UAVs and IoT devices and then evaluate the interference, the coverage probability, and the data rate of the typical UAV. To assess the harvesting capability of the proposed architecture, we derive a formula for the amount of data uploaded from each IoT device to a UAV. We also establish a linear relationship between the UAV coverage and the harvesting capability of the network, which provides insights into the design of the proposed harvesting scheme. In addition, we use our analytical results to numerically show that there exists a trade-off between the uploaded data and the size of the IoT scheduling window. Specifically, for a given UAV and IoT geometry, there exists an optimal scheduling window that maximizes the harvesting capability of the proposed network.

cs.IT↗

arXiv2020

Scaling Laws of Dense Multi-Antenna Cellular Networks

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 $λ$, under the assumption of independent and identically distributed (i.i.d.) channels. We start with the MISO case with $N_t(λ)$ transmit antennas and a single receive antenna and prove that the average SINR scales as $\frac{N_t(λ)}λ$ and the average ASE scales as $λ\log\left(1+\frac{N_t(λ)}λ\right)$. For the MIMO case with single-stream eigenbeamforming and $N_r(λ) \leq N_t(λ)$ receive antennas, we prove that the scaling laws of the conditional SINR and ASE are agnostic to $N_r(λ)$ and scale exactly the same as the MISO case. Hence, deploying multi-antenna BSs can help maintain non-zero per-user throughput and a corresponding linear increase in the ASE in dense cellular networks.

cs.IT↗