arXiv subjects

Nahuel Soprano-Loto

Publications and source records attributed to Nahuel Soprano-Loto.

8 recordsLinked to original sources

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

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↗

arXiv2024

Decision-Epoch Matters: Unveiling its Impact on the Stability of Scheduling with Randomly Varying Connectivity

A classical queuing theory result states that in a parallel-queue single-server model, the maximum stability region does not depend on the scheduling decision epochs, and in particular is the same for preemptive and non-preemptive systems. We consider here the case in which each of the queues may be connected to the server or not, depending on an exogenous process. In our main result, we show that the maximum stability region now does strongly depend on how the decision epochs are defined. We compare the setting where decisions can be made at any moment in time (the unconstrained setting), to two other settings: decisions are taken either (i) at moments of a departure (non-preemptive scheduling), or (ii) when an exponentially clock rings with rate $γ$. We characterise the maximum stability region for the two constrained configurations, allowing us to observe a reduction compared to the unconstrained configuration. In the non-preemptive setting, the maximum stability region is drastically reduced compared to the unconstrained setting and we conclude that a non-preemptive scheduler cannot take opportunistically advantage (in terms of stability) of the random varying connectivity. Instead, for the $γ$ decision epochs, we observe that the maximum stability region is monotone in the rate of the decision moments $γ$, and that one can be arbitrarily close to the maximum stability region in the unconstrained setting if we choose $γ$ large enough. We further show that Serve Longest Connected (SLC) queue is maximum stable in both constrained settings, within the set of policies that select a queue among the connected ones. From a methodological viewpoint, we introduce a novel theoretical tool termed a ``test for fluid limits'' (TFL) that might be of independent interest. TFL is a simple test that, if satisfied by the fluid limit, allows us to conclude for stability.

math.PR↗

arXiv2023

Online matching for the multiclass stochastic block model

We consider the problem of sequential matching in a stochastic block model with several classes of nodes and generic compatibility constraints. When the probabilities of connections do not scale with the size of the graph, we show that under the NCOND condition, a simple max-weight type policy allows to attain an asymptotically perfect matching while no sequential algorithm attain perfect matching otherwise. The proof relies on a specific Markovian representation of the dynamics associated with Lyapunov techniques.

math.PR↗

arXiv2020

Generalized max-weight policies in stochastic matching

We consider a matching system where items arrive one by one at each node of a compatibility network according to Poisson processes and depart from it as soon as they are matched to a compatible item. The matching policy considered is a generalized max-weight policy where decisions can be noisy. Additionally, some of the nodes may have impatience, i.e. leave the system before being matched. Using specific properties of the max-weight policy, we construct several Lyapunov functions, including a simple quadratic one. This allows us to establish stability results, to construct bounds for the stationary mean and variances of the total amount of customers in the system, and to prove exponential convergence speed towards the stationary measure. We finally illustrate some of these results using simulations on toy examples.

math.PR↗

arXiv2017

Turing instability in a model with two interacting Ising lines: hydrodynamic limit

This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time Markov process defined in terms of macroscopic Kac potentials and local interactions. For fixed time, we prove that the density fields weakly converge to the solution of a system of partial differential equations involving convolutions. The presence of local interactions results in the lack of propagation of chaos, reason why the hydrodynamic limit cannot be obtained from previous results.

math.PR↗

arXiv2017

Hydrodynamics of the $N$-BBM process

The Branching Brownian Motions (BBM) are particles performing independent Brownian motions in $\mathbb R$ and each particle at rate 1 creates a new particle at her current position; the newborn particle increments and branchings are independent of the other particles. The $N$-BBM starts with $N$ particles and at each branching time, the leftmost particle is removed so that the total number of particles is $N$ for all times. The $N$-BBM was proposed by Maillard and belongs to a family of processes introduced by Brunet and Derrida. We fix a density $ρ$ with a left boundary $L=\sup\{r\in\mathbb R: \int_r^\infty ρ(x)dx=1\}>-\infty$ and let the initial particle positions be iid continuous random variables with density $ρ$. We show that the empirical measure associated to the particle positions at a fixed time $t$ converges to an absolutely continuous measure with density $ψ(\cdot,t)$, as $N\to\infty$. The limit $ψ$ is solution of a free boundary problem (FBP) when this solution exists. The existence of solutions for finite time-intervals has been recently proved by Lee.

math.PR↗

arXiv2015

Phase transition for the dilute clock model

We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour $q$-state clock model in $\mathbb{Z}^d$, for every $q\geq 2$ and $d\geq 2$. This follows from the fact that the Edwards-Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applied to show phase transition for the low-temperature Potts model. The domination involves a combinatorial lemma which is one of the main points of this article.

math.PR↗