Pour voir le titre et le résumé de l’exposé, cliquez sur le nom de l'orateur(ice).
| exposé JCJC | 20' + 2' |
| exposé senior | 25' + 5' |
| Lundi, 2 décembre | Mardi, 3 décembre | Mercredi, 4 décembre | |
|---|---|---|---|
| 09:00 --- 10:30 | Anselmi Hyon Thiran |
Dhiman Soprano-Loto Hira Rigonat |
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| 10:30 --- 11:00 | Pause café | Pause café | |
| 11:00 --- 12:00 | Moyal Neglia |
Lelarge Touati |
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| 12:00 --- 13:30 | Déjeuner 13:20 Mot d'accueil |
Déjeuner | Déjeuner |
| 13:30 --- 15:00 | Baccelli El Ayoubi Comte |
Agarwal Mengoli Pierre El Mimouni |
Chaintreau Busic Tuffin |
| 15:00 --- 15:15 | Pause café | Pause café | |
| 15:15 --- 16:45 |
Avratchenkov (exposé long) |
Combes/Zhang Gast Anton |
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| 16:45 --- 17:00 | Pause café | Pause café | |
| 17:00 --- 18:00 | El Azouzi Fricker |
Table ronde | |
| 18:15 --- | Cocktail | Repas de gala |
Jonatha Anselmi
Asynchronous Load Balancing and Auto-scaling: Mean-field Limit and Optimal Design [slides]
We develop a Markovian framework for load balancing that combines classical algorithms such as Power-of-$d$ with auto-scaling mechanisms that allow the net service capacity to scale up or down in response to the current load on the same timescale as job dynamics. Our framework is inspired by serverless platforms, such as Knative, where servers are software functions that can be flexibly instantiated in milliseconds according to scaling rules defined by the users of the serverless platform. The main question is how to design such scaling rules to minimize user-perceived delay performance while ensuring low energy consumption. For the first time, we investigate this problem when the auto-scaling and load balancing processes operate *asynchronously* (or proactively), as in Knative. In contrast to the synchronous (or reactive) paradigm, asynchronism brings the advantage that jobs do not necessarily need to wait any time a scale-up decision is taken. In our main result, we find a general condition on the structure of scaling rules able to drive mean-field dynamics to delay and relative energy optimality, i.e., a situation where both the user-perceived delay and the relative energy waste induced by idle servers vanish in the limit where the network demand grows to infinity in proportion to the nominal service capacity. The identified condition suggests to scale up the current net capacity if and only if the mean demand exceeds the rate at which servers become idle and active. Finally, we propose a family of scaling rules that satisfy our optimality condition. Numerical simulations demonstrate that these rules provide better delay performance than existing synchronous auto-scaling schemes while inducing almost the same power consumption.
Elene Anton
Stability and performance of multi-class queueing systems with unknown service rates: A scheduling-based approach [slides]
We consider a system with N different service modes handling multiple traffic classes, where a scheduling agent decides which service option to use at each time slot. Each service mode provides service to all the traffic classes simultaneously, at different random rates (possibly zero). The scheduling agent can observe the global queue state, but does not have any advance knowledge of the instantaneous rates or service rate distributions associated with each of the service modes. We propose a threshold-based algorithm where the threshold value is compared to the sum of the square of the queue lengths at that time slot. If the threshold value is exceeded, then the scheduling agent switches the service mode, and it keeps using the same service mode otherwise. This sequential decision making process is related to the well-studied Multi-Armed Bandit problem or the Max-Weight algorithm but involves several major differences and additional challenges. We aim to understand the performance of this threshold-based scheduling algorithm: first, we show that the scheduling algorithm achieves maximum stability. We then analyse the mean response time of the different traffic classes.
Konstantin Avratchenkov
A Journey Through the History of Markov Chains
Markov chains, mathematical models that describe sequences of dependent events, were created to make a point in a philosophical discussion and to explain the beauty of the poetry. Even though we may debate the practicality of explanations of aesthetics, it is generally accepted that Andrey Markov (1856-1922) contributed to this philosophical dispute and, in the process, originated one of the most powerful tools of applied mathematics, physics and now artificial intelligence. In this talk, I overview the main stages of the exciting history of Markov chains.
François Baccelli
Phase transitions in unimodular random trees [slides]
The talk will survey recent results on unimodular random networks. The focus will be on a classification of dynamics on such networks in terms of global properties of trees built from their orbits. Several illustrations of this classification will be discussed. They will cover mathematical objects (e.g., random walks and renewal processes), algorithms (e.g., classification and unsupervised learning) and also real life questions (in particular evolution)
Ana Busic
Multi-agent reinforcement learning for wind farm control [slides]
Maximizing the energy production in wind farms requires mitigating wake effects, a phenomenon by which wind turbines create sub-optimal wind conditions for the turbines located downstream. Finding optimal control strategies is challenging, as high-fidelity models predicting complex aerodynamics are not tractable for optimization. Good experimental results have been obtained using a cooperative multi-agent reinforcement learning. In particular, independent learning approach lead to a significant increase of power output in simulated farms. Despite empirical success, the independent learning approach has no convergence guarantee due to non-stationarity. We show that the wind farm control problem can be framed as an instance of a transition-independent Decentralized Partially Observable Decentralized Markov Decision Process (Dec-POMDP) where the interdependence of agents dynamics can be represented by a directed acyclic graph (DAG). We show that for these problems, non-stationarity can be mitigated by a multi-scale approach, and show that a multi-scale Q-learning algorithm (MQL) where agents update local Q-learning iterates at different timescales guarantees convergence.
This is a joint work with Claire Bizon Monroc, Jiamin Zhu, and Donatien Dubuc.
This is a joint work with Claire Bizon Monroc, Jiamin Zhu, and Donatien Dubuc.
Richard Combes (replaced by Raymond Zhang)
Thompson Sampling For Combinatorial Bandits: Polynomial Regret and Mismatched Sampling Paradox [slides]
We consider Thompson Sampling (TS) for linear combinatorial semi-bandits and subgaussian rewards. We propose the first known TS whose finite-time regret does not scale exponentially with the dimension of the problem. We further show the “mismatched sampling paradox”: A learner who knows the rewards distributions and samples from the correct posterior distribution can perform exponentially worse than a learner who does not know the rewards and simply samples from a well-chosen Gaussian posterior. Joint work with Raymond Zhang.
Augustin Chaintreau
Fourniture et Échange de données équitables et efficace par Incitation [slides]
What is fair machine learning? How does it connect with performance and deployment goals in multi-party ecosystem (where data providers and platforms enabling data collection and exchange for firms that consume them for their operations)? What stands in the way of deployment of equitable algorithms or standards for data production? We argue that it often comes from the fact that incentives are overlooked. To support our thesis we present two theoretical results: First, we consider the fair data provision problem and theoretically prove an exponential gap in favor of incentive compatibility when it comes to controlling the cost of fairness. Second, we introduce a simple economic model of data standard deployment and prove that it preserves social welfare asymptotically in established markets with reuse, and show how it struggles with emerging markets.
Céline Comte
Routing Optimization for Asynchronous Federated Learning on Heterogeneous Resources [slides]
Synchronous federated learning (FL) scales poorly with the number of clients due to the straggler effect. To overcome this limitation, algorithms like FedAsync allow clients and the central server to communicate asynchronously, thus trading estimation errors for scalability and speed. While most existing analyses are based on overly simplified assumptions on delays, recent research highlights the crucial impact of these queuing dynamics on performance. Building on this insight, we make advances in both the analysis and optimization of asynchronous FL. We demonstrate that existing performance bounds can be expressed in closed form using stationary distributions of Jackson networks; in particular, this yields an explicit characterization of performance as a function of task-to-clients routing probabilities. In addition, we introduce a gradient-based optimization method to improve performance by adapting these routing probabilities. Lastly, we show that existing performance bounds do not adequately account for convergence rates relative to clock time, and we propose an alternative metric that addresses this limitation. Several experiments illustrate the performance gains of routing optimization.
This is joint work with Abdelkrim Alahyane, Matthieu Jonckheere and Éric Moulines.
Salah El Ayoubi
Reliable communications in 5G and 6G networks: from URLLC to haptic communications [slides]
Ultra reliability has been a main driver for the definition of the radio interface for 5G networks. The Ultra Reliable Low Latency Communications (URLLC) service targeted novel applications such as connected and autonomous cars and remote control of machines. A tremendous amount of research works have addressed URLLC performance, and we will focus in the first part of this talk on queuing theoretical models. With the definition of 6G networks, new delay sensitive services are being discussed, including extreme URLLC and haptic communications, tailored towards Metaverse applications. We present in the second part of the talk the requirements and performance models for these new services and explore the promising research direction of goal-oriented communications and the joint design of the network and control systems.
Rachid El Azouzi
Optimal client sampling for multi-model federated learning
Federated learning (FL) is a variant of distributed learning in which multiple clients collaborate to learn a global model without sharing their data with the central server. In real-world scenarios, a client may be involved in training multiple unrelated FL models, which we call multi-model federated learning (MMFL), and the client sampling strategy and task allocation are crucial for improving system performance. We start by designing a learning process for a heterogeneous MMFL system, proving it guarantees unbiased convergence. Motivated by this analysis, we propose two client-model allocation methods to accelerate convergence for all models. Our analysis shows these methods perform well, but their client participation variability slows convergence. To mitigate this, we propose a variant of our aggregation method that reuses stale client updates. Finally, we propose a client sampling variant ensuring fair training progress for models with heterogeneous difficulty levels. Extensive experiments show our MMFL algorithms outperform several baselines.
Christine Fricker
Approximation of large bike/car sharing systems [slides]
We use that these systems can be modelled by closed Jackson networks with blocking and rerouting policy when nodes with finite capacity are saturated. This dynamics preserves the product from (on non-product space) of the underlying invariant distribution. Using a Local limit theorem for independent non identically distributed random variables, one can obtain asymptotic independence of a finite subset of nodes as the system gets large. The asymptotic stationary distribution at the nodes is explicit. It is used to discuss the fleet size which gives a good trade-off between finding a bike or a parking space. Extensions to car-sharing (with car reservation) are presented.
Joint works with Danielle Tibi, Hanene Mohamed and Alessia Rigonat.
Nicolas Gast
Asymptotic Optimality in Restless Bandit. [slides]
Restless bandit and weakly coupled MDPs are classical modeling tools to model resource allocation problems (for instance in scheduling or queuing networks). These problems are computationally hard to solve and there has been a number of heuristics proposed in the literature, based on linear relaxation and mean field control. While some of them date from the 90s (the famous Whittle index), there has been a surge of recent development in this area. This talk will discuss these later developments: the what, the how and the why.
Joint work with Bruno Gaujal, Dheeraj Narasimha, and Chen Yan
Emmanuel Hyon
Reinforcement Learning for Service Placement and Routing under Delay Constraint [slides]
We present a network optimization problem related to the placement of Software as a Service (SaaS) in an Edge Computing network architecture. We model this problem as a multi-commodity flow problem with service placement under a delay constraint. We compare different solving approaches: a compact linear formulation, various heuristics that enable much faster solving times, and a new approach that uses Deep Reinforcement Learning, which outperforms the previous approaches on larger instances.
Marc Lelarge
Chaining Graph Neural Networks to learn the graph alignment problem [slides]
We explore the power of graph neural networks (GNNs) for solving a combinatorial optimization problem: the graph alignment problem, which aims to match unlabeled graphs using only topological information.In a supervised setting, we train GNNs to enhance a partial solution so that during inference, the GNNs are chained to bootstrap the performance.We show that our chaining procedure can be coupled with an existing solver based on the Frank-Wolfe algorithm as a last step to allow us to recover the optimal solution in cases where no other algorithm is able to do so.
Pascal Moyal
Optimization and control of dynamic matching systems [slides]
In this talk, we present an optimization result regarding the control over time of a simple stochastic matching model with holding cost. We use the tools of dynamic programming to show that a ‘threshold’-type policy is optimal for discounted costs. Second, we investigate the question of access control of such models under the ‘First Come, First Matched’ matching policy, and show how ‘Policy-gradient’ type algorithms may allow, using the product-form of the stationary distribution, to optimize the admission probability.
This talk is based on joint works with Loïc Jean and Céline Comte.
Giovanni Neglia
Scalable Decentralized Algorithms for Online Personalized Mean Estimation [slides]
In numerous settings, agents lack sufficient data to learn a model directly. Collaborating with other agents may help, but introduces a bias-variance trade-off when local data distributions differ. A key challenge is for each agent to identify clients with similar distributions while learning the model, a problem that remains largely unresolved. This study focuses on a particular instance of the overarching problem, where each agent collects samples from a real-valued distribution over time to estimate its mean. Existing algorithms face impractical per-agent space and time complexities (linear in the number of agents |A|). To address scalability challenges, we propose a framework where agents self-organize into a graph, allowing each agent to communicate with only a selected number of peers r. We propose two collaborative mean estimation algorithms: one employs a consensus-based approach, while the other uses a message-passing scheme, with complexity O(r) and O(r · log |A|), respectively. We establish conditions for both algorithms to yield asymptotically optimal estimates and we provide a theoretical characterization of their performance.
Patrick Thiran
Network Community Structure under Metric Sparsification [slides]
Graph sparsification replaces a graph by a sparser copy, with fewer vertices and/or edges, to reduce storage and/or computational costs while preserving (some) structural properties. We consider here weighted graphs, and sparsify them by keeping the same vertex set but by reducing their edge set to their metric backbone. The metric backbone of a weighted graph is the union of all-pairs shortest paths, and is obtained by removing all edges (u,v) that do not lie on the shortest path between vertices u and v. In networks with well-separated communities, the metric backbone tends to preserve many inter-community edges, because these edges serve as bridges connecting two communities, but tends to delete many intra-community edges because the communities are dense. This suggests that the metric backbone might not preserve the community structure of the network. However, prior empirical work showed instead that the metric backbone of real-world networks preserves the community structure of the original network. In this work, we analyze the metric backbone of a broad class of weighted random graphs with communities, and we prove the robustness of the community structure with respect to the deletion of all the edges that are not in the metric backbone. An empirical comparison shows that the metric backbone is an effective graph sparsifier in the presence of communities.
This is a joint work with Maximilien Dreveton, Charbel Chucri and Matthias Grossglauser.
Mikaël Touati
Solving Random Regular Parity Games in Polynomial Time [slides]
We consider the problem of solving random regular parity games and show that there exists a threshold such that if graph of the game has a greater degree there is a polynomial time algorithm solving the game (and computing winning strategies) with high probability when the number of nodes tends to infinity. Particularly, we propose the algorithm SWCP (Self-Winning Cycles Propagation) with quadradic complexity and show that, when the degree is large enough, SWCP solves the game. The asymptotic properties of SWCP rely upon the emergence cycles in the players' respective sub-graphs.
Joint work with Richard Combes.
Bruno Tuffin
On Confidence Intervals for Randomized Quasi-Monte Carlo Estimators [slides]
Randomized quasi-Monte Carlo (RQMC) converges faster than standard Monte Carlo ones as the sample size increases, taking advantage of the repartition of quasi-Monte Carlo points. To get an idea of the estimation error, confidence intervals are usually built based on a central limit theorem (CLT) over independent randomizations. For a given computational budget, it means to increases the number of randomizations, limiting the size of the QMC sequence, hence its accuracy. During this talk, we will describe the challenges of building confidence intervals: we describe the existing CLTs, sufficient conditions on the relative growth rates of the number of randomizations and the quasi-Monte Carlo sequence length to ensure a central limit theorem and also an asymptotically valid confidence interval. We also compare numerically the Student t approach with two bootstrap methods for getting nonparametric confidence intervals for the mean using a modest number of replicates.
Khushboo Agarwal
Games among selfish and team stations in polling systems [slides]
Queues are everywhere; therefore, it is no surprise that the study of queuing systems is rich today. The polling system is a particular queuing system that caters to several applications like computer networks, telecommunications, production systems, traffic and transportation systems, and will be the topic of interest. We will focus on a particular polling system known as the cyclic Bernoulli polling (CBP) system, where a server moves cyclically between the stations and serves the queue at a station with a certain probability when polled. Each station follows either gated or partially exhaustive service discipline. In the steady state of such a system, we study a new game-theoretic aspect, where, the stations strategically choose the probability of accepting or rejecting the service from the server when polled. We examine three variants of non-cooperative games among stations: (i) each station selfishly minimizes its expected waiting time, (ii) a team game where each station minimizes the expected workload of the system, and (iii) stations act with partial cooperation, incurring an additional linear cost. We begin by presenting a new result for the CBP system regarding the continuity of expected waiting times in relation to the probabilities selected by the stations. For each game, we then investigate the existence and uniqueness of the Nash equilibrium (NE). In some cases, the NE is explicitly derived, while in others, characterizing the NE remains challenging due to the complex dependence of waiting times on the non-trivial buffer occupancy equations. Nonetheless, we analyze the NE and its properties through numerical experiments. Notably, in many instances, stations opt to accept service with a probability less than 1 --- a trend observed even among selfish stations.
Ashutosh Balakrishnan
Achieving energy sustainability and scalability: Exploring joint load and energy balancing based network design [slides]
Realizing energy sustainable communication networks has been a key challenge in the upcoming sixth generation (6G) networks. A key bottleneck has been to make the energy-efficient network solutions industrially attractive and scalable, thereby necessitating a techno-economic analysis. Through this talk, the prospects of achieving energy sustainability as well as cost profitability through ambient powered and grid connected communication framework is analyzed and studied. The power grid connectivity plays a vital role in achieving the aforesaid objective, alongside ambient powered base stations (BSs). The networked system is further analyzed to outlay the challenges, physical constraints, and network operations involved in optimizing the system. As a case study, the talk outlines the importance of energy balancing in networks, and showcases the benefit of joint load-energy balancing in networks in contrast to the traditional load balancing paradigm.
Madhu Dhiman
Interplay Between Epidemic and News Propagation Processes [slides]
The COVID-19 pandemic has witnessed the role of online social networks (OSNs) in the spread of infectious diseases. The rise in severity of the epidemic augments the need for proper guidelines but also promotes the propagation of fake news-items. The popularity of a news-item can reshape public health behaviours and affect the epidemic processes. There is a clear inter-dependency between the epidemic process and the spreading of news-items. This work creates an integrative framework to understand the interplay. We first develop a population-dependent ‘saturated branching process’ to continually track the propagation of trending news-items on OSNs. A two-time scale dynamical system is obtained by integrating the news-propagation model with the SIRS epidemic model to analyze the holistic system. It is observed that a pattern of periodic infections emerges under a linear behavioural influence, which explains the waves of infection and reinfection that we have experienced during the pandemic. We use numerical experiments to corroborate the results and use Twitter and COVID-19 data-sets to recreate the historical infection curve using the integrative model.
Ibtihal El Mimouni
Deep Q-Learning with Whittle Index for Contextual Restless Multi-Armed Bandits [slides]
The Multi-Armed Bandit (MAB) problem is a classic framework in decision theory, where an agent aims to maximize cumulative reward by balancing exploration of unknown arms with exploitation of arms expected to be more rewarding. Restless Multi-Armed Bandits (RMAB) extend this model by allowing arm states to evolve over time, regardless of whether they are selected. This dynamic nature significantly increases complexity, as finding optimal policies for general RMAB is PSPACE-hard. The Whittle index, a heuristic approach, has shown promise in addressing the complexity of RMAB. Contextual Restless Multi-Armed Bandits (CRMAB) further extend this framework by incorporating contextual information, such that each arm is modeled as a context-augmented Markov decision process. The context influences both reward and state transition probabilities, which makes CRMAB well-suited for modeling real-world scenarios with changing environments. Within this framework, we introduce DQWIC (Deep Q-learning the Whittle Index with Context), a novel algorithm that combines Deep Reinforcement Learning and Whittle index theory. DQWIC leverages two neural networks: a Q-network that approximates action-value functions (Q-values), and a Whittle-network that estimates Whittle indices. The learning process occurs through a two time scale stochastic approximation, with the Q-network updated frequently to minimize the loss between the predicted and the target Q-values, and the Whittle-network updated on a slower time scale. To demonstrate DQWIC's effectiveness, we apply it to an email recommender system. Each arm represents a potential email recipient, with states reflecting user engagement levels and contexts including campaign and user-related features. Our experimental results, derived from both synthetic and real-world data, show that DQWIC outperforms existing baselines.
Emanuele Mengoli
Dynamic Bayesian Optimization for Improving the Performance of Cellular Networks [slides]
With increasing complexity in wireless communication networks, innovative strategies are needed to enhance their efficiency and adaptability. This project investigates Bayesian Optimization (BO) for resource allocation optimization in dynamic wireless cellular networks, specifically utilizing Non-Orthogonal Multiple Access (NOMA) as the resource-sharing mechanism (RSM). Traditional greedy search methods can hinder effective decision-making due to the high computational cost of performance evaluations. Our approach leverages a new BO algorithm, Wasserstein-Dynamic Bayesian Optimization (W-DBO) [1], designed to interplay with settings subjected to spatio-temporal dynamics.
This is a joint work with Anthony Bardou and Patrick Thiran from EPFL.
[1] Bardou, Anthony, Patrick Thiran, and Giovanni Ranieri. “This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization.” arXiv preprint arXiv:2405.14540
This is a joint work with Anthony Bardou and Patrick Thiran from EPFL.
[1] Bardou, Anthony, Patrick Thiran, and Giovanni Ranieri. “This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization.” arXiv preprint arXiv:2405.14540
Thomas Hira
Non-Preemptive Scheduling in Non-Observable Environments [slides]
We address the problem of optimal non-preemptive scheduling in a queueing system where service availability is modeled by Gilbert-Elliot channels. The channel states are not directly observable, requiring the use of belief states for scheduling decisions. Our objective is to determine policies that maximize the long-run average reward under non-preemptive constraints. We derive non-preemptive scheduling policies for both positively and negatively autocorrelated queues, analyzing various configurations such as asymmetric (including symmetric) cases for positively autocorrelated queues and symmetric, negatively autocorrelated cases restricted to two queues. Furthermore, we evaluate the impact of limited observability and non-preemptive constraints by comparing our results with fully observable and preemptive versions of the model, highlighting the inherent trade-offs and performance implications.
Marc Pierre
Optimal control for resource allocation in a discrete queuing system. [slides]
Markov decision processes are a set of random processes that can be used to model environments that can be transformed by actions in order to receive gains. The theory surrounding these processes gives us different conditions for finding a strategy that maximizes strategy under certain criteria. Our aim is to control a discrete queue model, where the control is the number of customers processed in the queue. In this presentation, we'll look at how to reduce the search space for optimal policies, and then exploit this structure to solve the problem quickly.
Frédy Pokou
Noncooperative Games with Prospect Theoretic Preferences [slides]
We study noncooperative stochastic games, where agents display irrational behaviors in response to underlying risk factors. Our formulation incorporates Prospect Theory (PT), a behavioral model used to describe agents’ risk attitude, into the equilibrium theory of noncooperative N-agent games. We show that the resulting nonconvex nonsmooth game admits equilibria and provide conver- gence guarantees for their computation. Further, the concept of “Price of Irrationality” is introduced to quantify the suboptimality induced by irrational behaviors. Finally, we provide bounds on the perfor- mance of a class of PTaggregative games and illustrate our results on an electricity market involving strategic end users exposed to risk.
Alessia Rigonat
Mean-field analysis of a multi-scale stochastic model for free-floating car sharing [slides]
We consider a large set of nodes, each with fixed but large capacity. A node can be occupied either by internal customers, who move within the system, or by external customers, who can enter and leave the system and are considered the environment. We are interested in the mean-field limit of internal customers, in interaction with the random environment. The main feature of the model is that, in each node, the environment evolves on a faster time scale than internal customers. A phase transition is achieved between an underloaded regime where internal customers can enter a site with probability 1, and an overloaded regime where they can be rejected with positive probability. The model is motivated by free-floating car-sharing, where cars of the system share parking spaces with private cars. Our result shows that the operator can increase the fleet size without reducing the number of available public parking spaces, even if these are limited. Therefore the performance of the system can be measured in terms of vehicle availability only. We analyze it for different choices of the customers routing function.
Joint work with Christine Fricker and Hanene Mohamed.
Joint work with Christine Fricker and Hanene Mohamed.
Nahuel Soprano-Loto
La valeur des époques de décision dans les systèmes de files d'attente avec des connectivités aléatoires [slides]
Dans le cadre d'un modèle de file d'attente parallèle avec un seul serveur, dans lequel les files d'attente peuvent être connectées de manière aléatoire au serveur, nous étudions comment les restrictions de timing sur les époques de planification affectent la performance du système. Plus précisément, nous analysons trois configurations : (i) sans contraintes, (ii) non préemptive, et (iii) avec décisions à des instants exponentiellement distribués. Pour chacune d'elles, nous fournissons des descriptions explicites des régions de stabilité maximale. Ces modèles sont efficaces pour les réseaux de communication sans fil, où les connectivités aléatoires représentent la présence d'obstacles entre l'utilisateur et la station de base, et les époques de décision représentent des créneaux horaires « à optimiser » pour les actions. Les démonstrations mathématiques s'appuient sur une analyse de limite fluide, avec toutefois un raccourci qui nous permet de conclure plus directement. Il s'agit d'un travail en collaboration avec U. Ayesta (IRIT-CNRS), M. Jonckheere (LAAS-CNRS) et I.M. Verloop (IRIT-CNRS).
