224 research outputs found
A stochastic network with mobile users in heavy traffic
No full textWe consider a stochastic network with mobile users in a heavy traffic regime. We derive the scaling limit of the multidimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by Lambert and Simatos (preprint, 2012), which provides a general principle to establish scaling limits of regenerative processes based on the convergence of their excursions. We also prove weak convergence of the sequences of stationary joint queue length distributions and stationary sojourn times
A stochastic network with mobile users in heavy traffic
No full textWe consider a stochastic network with mobile users in a heavy traffic regime. We derive the scaling limit of the multidimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by Lambert and Simatos (preprint, 2012), which provides a general principle to establish scaling limits of regenerative processes based on the convergence of their excursions. We also prove weak convergence of the sequences of stationary joint queue length distributions and stationary sojourn times
A variant of the Recoil Growth algorithm to generate multi-polymer systems
No full textInternational audienceThe Recoil Growth algorithm, proposed in 1999 by Consta , is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding paths. In this paper, we study a variant of the original Recoil Growth algorithm, where we constrain the generation of a new polymer to take place on a specific class of graphs. This makes it possible to make a fine trade-off between computational cost and success rate. We moreover give a simple proof for a lower bound on the irreducibility of this new algorithm, which applies to the original algorithm as well
Spatial homogenization in a stochastic network with mobility
No full textA stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes, where they receive service according to the Processor-Sharing policy. Once their service requirement is satisfied, they leave the system. The stability region is identified via a fluid limit approach, and strongly relies on a ``spatial homogenization'' property: At the fluid level, customers are instantaneously distributed across the network according to the stationary distribution of their Markovian dynamics and stay distributed as such as long as the network is not empty. In the unstable regime, spatial homogenization almost surely holds asymptotically as time goes to infinity (on the normal scale), telling how the system fills up. One of the technical achievements of the paper is the construction of a family of martingales associated to the multidimensional process of interest, which makes it possible to get crucial estimates for certain exit times
Differential impact of dose-range glyphosate on locomotor behavior, neuronal activity, glio-cerebrovascular structures, and transcript regulations in zebrafish larvae
No full textThe presence of glyphosate represents a debated ecotoxicological and health risk factor. Here, zebrafish larvae were exposed, from 1.5 to 120 h post-fertilization, to a broad concentration range (0.05–10.000 μg/L) of glyphosate to explore its impact on the brain. We evaluated morphology, tracked locomotor behavior and neurophysiological parameters, examined neuro-glio-vascular cell structures, and outlined transcriptomic outcomes by RNA sequencing. At the concentration range tested, glyphosate did not elicit gross morphological changes. Behavioral analysis revealed a significant decrease in locomotor activity following the exposure to 1000 μg/L glyphosate or higher. In parallel, midbrain electrophysiological recordings indicated abnormal, and variable, spike activity in zebrafish larvae exposed to 1000 μg/L glyphosate. Next, we asked whether the observed neurophysiological outcome could be secondary to brain structural modifications. We used transgenic zebrafish and in vivo 2-photon microscopy to examine, at the cellular level, the effects of the behavior-modifying concentration of 1000 μg/L, comparing to low 0.1 μg/L, and control. We ruled out the presence of cerebrovascular and neuronal malformations. However, microglia morphological modifications were visible at the two glyphosate concentrations, specifically the presence of amoeboid cells suggestive of activation. Lastly, RNAseq analysis showed the deregulation of transcript families implicated in neuronal physiology, synaptic transmission, and inflammation, as evaluated at the two selected glyphosate concentrations. In zebrafish larvae, behavioral and neurophysiological defects occur after the exposure to high glyphosate concentrations while cellular and transcript signatures can be detected in response to low dose. The prospective applicability to ecotoxicology and the possible extension to brain-health vulnerability are critically discussed
A Queueing System for Modeling a File Sharing Principle
No full textInternational audienceWe investigate in this paper the performance of a simple file sharing principle. For this purpose, we consider a system composed of N peers becoming active at exponential random times; the system is initiated with only one server offering the desired file and the other peers after becoming active try to download it. Once the file has been downloaded by a peer, this one immediately becomes a server. To investigate the transient behavior of this file sharing system, we study the instant when the system shifts from a congested state where all servers available are saturated by incoming demands to a state where a growing number of servers are idle. In spite of its apparent simplicity, this queueing model (with a random number of servers) turns out to be quite difficult to analyze. A formulation in terms of an urn and ball model is proposed and corresponding scaling results are derived. These asymptotic results are then compared against simulations
Coupling limit order books and branching random walks
No full textWe consider a model for a one-sided limit order book proposed by Lakner et al. and show that it can be coupled with a branching random walk. We then use the coupling to answer non-trivial questions about the long-term behavior of the price. The coupling relies on a classical idea of enriching the state-space by artificially creating a filiation, in this context between orders of the book, that we believe has the potential of being useful for a broader class of model
Étude de modèles probabilistes de réseaux pair-à-pair et de réseaux avec mobilité
No full textThe goal of this thesis is to solve four problems motivated by modern com- munication networks; the appropriate tools to solve these problems belong to the theory of probability. Solving these problems gives insight into the original physi- cal systems, and contributes at the same time to the theory since new theoretical results of independent interest are proved. Two kinds of communication networks are considered. Mobile networks are these networks where customers perform trajectories within the network indepen- dently of the service they receive; in contrast with classical queueing networks, transitions of customers are not triggered by service completions. In peer-to-peer networks the distinction between clients and servers is abolished, since in these net- works a server is a former client that offers a file once it has downloaded it. These last networks are especially efficient in spreading large or popular files. In Chapters I and II, the stationary behavior of such networks is considered. In each case, one describes the network through a discrete state-space, continuous time Markov process, and establishes its ergodicity or transience. A specificity of these two models is that the transition rates of the corresponding Markov processes are unbounded: in the case of the mobile network of Chapter I this is due to the fact that customers move independently of one another, while for the peer-to-peer network of Chapter II this is because the capacity of the system is proportional to the number of customers. Classically, to analyze the stability of a stochastic network, one can study the limits of a sequence of suitably rescaled Markov processes, the so-called fluid limits. This scaling is well suited for “locally additive” processes, i.e., processes which lo- cally behave as random walks; this is however not the case when the transition rates are unbounded. These techniques are nonetheless adapted to study the stability of the mobile network of Chapter I: using fluid limits to study the stability of Markov processes with unbounded transition rates represents one of the contributions of this work. The peer-to-peer network of Chapter II is not amenable to the same techniques, and Lyapounov type arguments are used. Another additional key ingredient is re- lated to a special class of branching processes. These new branching processes are defined and studied in Chapter II, and estimates on their extinction time make it possible, thanks to coupling arguments, to derive stability results on the stochastic network. In addition to the stationary behavior of peer-to-peer networks, their transient behavior can also be studied: this is the object of the simple model of Chapter III.Le but de cette thèse est de traiter quatre problèmes motivés par les réseaux de communication modernes ; les outils appropriés pour résoudre ces problèmes ap- partiennent à la théorie des probabilités. La résolution de ces problèmes améliore la compréhension des systèmes physiques initiaux, et contribue en même temps à la théorie puisque de nouveaux résultats théoriques, intéressants en soi, sont prouvés. Deux types de réseaux de communication sont considérés. Les réseaux mobiles sont ces réseaux où les clients se déplacent dans le réseau indépendamment du service qu'ils reçoivent ; contrairement aux réseaux de files d'attente classiques, les transitions des clients ne sont pas liées aux fins de service. Dans les réseaux pair- à-pair, la distinction entre client et serveur est abolie, puisque dans ces réseaux un serveur est un ancien client qui offre le fichier après l'avoir téléchargé. Ces derniers réseaux sont particulièrement efficaces pour disséminer des fichiers gros ou popu- laires. Dans les Chapitres I et II, le comportement stationnaire de tels réseaux est considéré. Dans chaque cas, le réseau est décrit par un processus de Markov à espace d'état discret et à temps continu, et l'on s'intéresse à son ergodicité ou au contraire à sa transience. Une spécificité de ces deux modèles est que les taux de transition des processus de Markov correspondants sont non bornés : dans le cas du réseau mobile du Chapitre I ceci est dû au fait que les clients bougent indépendamment les uns des autres, alors que pour le réseau pair-à-pair du Chapitre II, cela tient au fait que la capacité du système est proportionnelle au nombre de clients. Habituellement, l'analyse de la stabilité d'un réseau stochastique se fait par l'étude des limites d'une suite de processus de Markov correctement renormalisés, appelées limites fluides. Cette procédure est bien adaptée pour les processus “locale- ment additifs”, i.e., les processus qui se comportent localement comme des marches aléatoires ; cette propriété disparaît quand les taux de transition sont non bornés. Ces techniques sont néanmoins adaptées pour étudier la stabilité du réseau mobile du Chapitre I : utiliser des limites fluides pour étudier la stabilité de processus de Markov avec des taux de transition non bornés représente l'une des contributions de ce travail. Le réseau pair-à-pair du Chapitre II ne se prête quant à lui pas à ces tech- niques, et la stabilité découle alors de l'existence d'une fonction de Lyapounov. Un autre ingrédient clef est lié à une classe spéciale de processus de branchement. Ces nouveaux processus de branchement sont définis et étudiés dans le Chapitre II, et des estimations sur leur temps d'extinction permettent, avec des arguments de cou- plage, d'établir des résultats de stabilité du réseau stochastique. Outre le comportement stationnaire des réseaux pair-à-pair, leur comportement transient peut aussi être étudié : ce comportement est l'objet du modèle simple du Chapitre III. Ce modèle se concentre sur l'initialisation d'un réseau pair-à-pair dans un scénario d'arrivée en masse : au temps t = 0, un pair propose un nouveau fichier que N autres pairs veulent télécharger. Contrairement au modèle du Chapitre II, ici le flot d'arrivée de nouvelles requêtes n'est pas stationnaire, il est initialement très intense puis le devient de moins en moins. Bien que le système démarre avec un serveur et beaucoup de clients, le nombre de serveurs disponibles augmente avec le temps et l'on s'intéresse au temps nécessaire pour que le réseau se mette à niveau avec la grande demande initiale. Ce problème engendre un problème de boules et d'urnes intéressant en soi, qui est traité dans le Chapitre IV. Dans ce problème de boules et d'urnes, la distribution de probabilité qui décrit la manière dont les boules sont jetées est aléatoire : il s'agit donc d'un problème de boules et d'urnes en environnement aléatoire. De plus, les boules sont jetées dans un nombre infini d'urnes. Les problèmes de boules et d'urnes avec une infinité d'urnes sont bien étudiés, mais les résultats sur les problèmes de boules et d'urnes en environnement aléatoire sont peu nombreux. Quand il y a une infinité d'urnes, on peut s'intéresser à des quantités géométriques telle que l'emplacement de la première urne vide. De telles quantités ont parfois été étudiées dans des travaux antérieurs, en environnement déterministe : ici, grâce à l'utilisation de processus ponctuels, nous décrivons d'un coup tout le paysage des premières urnes vides, ce qui diffère des travaux précédents. En résumé, cette thèse contribue à la modélisation des réseaux mobiles et pair- à-pair ; d'un point de vue technique, des problèmes liés à la stabilité des processus de Markov, aux processus de branchement et aux problèmes de boules et d'urnes sont résolus
Occupancy Schemes Associated to Yule Processes
No full textAn occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the landscape of first empty bins, i.e., the set of corresponding indices represented by point processes, is analyzed and convergences in distribution to mixed Poisson processes are established. Additionally, the influence of the random environment, the random probability vector, is analyzed. It is represented by two main components: an i.i.d.\ sequence and a fixed random variable. Each of these components has a specific impact on the qualitative behavior of the stochastic model. It is shown in particular that for some values of the parameters, some rare events, which are identified, play an important role on average values of the number of empty bins in some regions
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