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International audience; We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively $\alpha$-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. We use this equivalence to show that for $\alpha > 0$, the asymptotic outcome concentrates around the optimum in a certain limiting sense when 'annealed' by letting $\alpha \to \infty$ slowly.

In this work, we study the spectrum of the normalized Laplacian and its regularized version for random geometric graphs (RGGs) in various scaling regimes. Two scaling regimes are of special interest, the connectivity and the thermodynamic regime. In the connectivity regime, the average vertex degree grows logarithmically in the graph size or faster. In the thermodynamic regime, the average vertex degree is a constant. We introduce a deterministic geometric graph (DGG) with nodes in a grid and provide an upper bound to the probability that the Hilbert–Schmidt norm of the difference between the normalized Laplacian matrices of the RGG and DGG is greater than a certain threshold in both the connectivity and thermodynamic regime. Using this result, we show that the RGG and DGG normalized Laplacian matrices are asymptotically equivalent with high probability (w.h.p.) in the full range of the connectivity regime. The equivalence is even stronger and holds almost surely when the average vertex degree $$a_n$$ a n satisfies the inequality $$a_n > 24 \log (n).$$ a n > 24 log ( n ) . Therefore, we use the regular structure of the DGG to show that the limiting eigenvalue distribution of the RGG normalized Laplacian matrix converges to a distribution with a Dirac atomic measure at zero. In the thermodynamic regime, we approximate the eigenvalues of the regularized normalized Laplacian matrix of the RGG by the eigenvalues of the DGG regularized normalized Laplacian and we provide an error bound which is valid w.h.p. and depends upon the average vertex degree.

The Proceedings of the ACM on Measurement and Analysis of Computing Systems (POMACS) focuses on the measurement and performance evaluation of computer systems and operates in close collaboration with the ACM Special Interest Group SIGMETRICS. All papers in this issue of POMACS will be presented at the ACM SIGMETRICS 2023 conference on June 19-23, 2023, in Orlando, Florida, USA. These papers have been selected during the winter submission round by the 91 members of the ACM SIGMETRICS 2023 program committee via a rigorous review process. Each paper was conditionally accepted (and shepherded), allowed a "one-shot" revision (to be resubmitted to one of the subsequent three SIGMETRICS deadlines), or rejected (with re-submission allowed after a year). For this issue, which represents the winter deadline, POMACS is publishing 11 papers out of 130 submissions. All submissions received at least 3 reviews and borderline cases were extensively discussed during the online program committee meeting. Based on the indicated track(s), roughly 28% of the submissions were in the Theory track, 44% were in the Measurement & Applied Modeling track, 43% were in the Systems track, and 22% were in the Learning track. Many individuals contributed to the success of this issue of POMACS. First, we would like to thank the authors, who submitted their best work to SIGMETRICS/POMACS. Second, we would like to thank the program committee members who provided constructive feedback in their reviews to authors and participated in the online discussions and program committee meeting. We also thank the several external reviewers who provided their expert opinion on specific submissions that required additional input. We are also grateful to the SIGMETRICS Board Chair, Giuliano Casale, and to past program committee Chairs, Niklas Carlsson, Edith Cohen, and Philippe Robert, who provided a wealth of information and guidance. Finally, we are grateful to the Organization Committee and to the SIGMETRICS Board for their ongoing efforts and initiatives for creating an exciting program for ACM SIGMETRICS 2023.

The Proceedings of the ACM on Measurement and Analysis of Computing Systems (POMACS) focuses on the measurement and performance evaluation of computer systems and operates in close collaboration with the ACM Special Interest Group SIGMETRICS. All papers in this issue of POMACS will be presented at the ACM SIGMETRICS 2023 conference on June 19-23, 2023, in Orlando, Florida, USA. These papers have been selected during the fall submission round by the 91 members of the ACM SIGMETRICS 2023 program committee via a rigorous review process. Each paper was conditionally accepted (and shepherded), allowed a "one-shot" revision (to be resubmitted to one of the subsequent three SIGMETRICS deadlines), or rejected (with re-submission allowed after a year). For this issue, which represents the fall deadline, POMACS is publishing 26 papers out of 119 submissions. All submissions received at least 3 reviews and borderline cases were extensively discussed during the online program committee meeting. Based on the indicated track(s), roughly 21% of the submissions were in the Theory track, 40% were in the Measurement & Applied Modeling track, 29% were in the Systems track, and 39% were in the Learning track. Many individuals contributed to the success of this issue of POMACS. First, we would like to thank the authors, who submitted their best work to SIGMETRICS/POMACS. Second, we would like to thank the program committee members who provided constructive feedback in their reviews to authors and participated in the online discussions and program committee meeting. We also thank the several external reviewers who provided their expert opinion on specific submissions that required additional input. We are also grateful to the SIGMETRICS Board Chair, Giuliano Casale, and to past program committee Chairs, Niklas Carlsson, Edith Cohen, and Philippe Robert, who provided a wealth of information and guidance. Finally, we are grateful to the Organization Committee and to the SIGMETRICS Board for their ongoing efforts and initiatives for creating an exciting program for ACM SIGMETRICS 2023.

International audience; This book is a general introduction to the statistical analysis of networks, and can serve both as a research monograph and as a textbook. Numerous fundamental tools and concepts needed for the analysis of networks are presented, such as network modeling, community detection, graph-based semi-supervised learning and sampling in networks. The description of these concepts is self-contained, with both theoretical justifications and applications provided for the presented algorithms.Researchers, including postgraduate students, working in the area of network science, complex network analysis, or social network analysis, will find up-to-date statistical methods relevant to their research tasks. This book can also serve as textbook material for courses related to the statistical approach to the analysis of complex networks.In general, the chapters are fairly independent and self-supporting, and the book could be used for course composition "à la carte". Nevertheless, Chapter 2 is needed to a certain degree for all parts of the book. It is also recommended to read Chapter 4 before reading Chapters 5 and 6, but this is not absolutely necessary. Reading Chapter 3 can also be helpful before reading Chapters 5 and 7.

We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when one orbit is tight but the other orbit goes to infinity in probability. All theoretical results are illustrated by numerical experiments.

The Proceedings of the ACM on Measurement and Analysis of Computing Systems (POMACS) focuses on the measurement and performance evaluation of computer systems and operates in close collaboration with the ACM Special Interest Group SIGMETRICS. All papers in this issue of POMACS will be presented at the ACM SIGMETRICS 2023 conference on June 19-13, 2023, in Orlando, Florida, USA. These papers have been selected by the 82 members of the ACM SIGMETRICS 2023 program committee via a rigorous review process. Each paper was conditionally accepted (and shepherded), allowed a "one-shot" revision (to be resubmitted to one of the subsequent three SIGMETRICS deadlines), or rejected (with re-submission allowed after a year). For this issue, which represents the summer deadline, POMACS is publishing 17 papers out of 93 submissions. All submissions received at least 3 reviews and borderline cases were extensively discussed during the online program committee meeting. Based on the indicated track(s), roughly 30% of the submissions were in the Theory track, 39% were in the Measurement Applied Modeling track, 33% were in the Systems track, and 29% were in the Learning track. Many individuals contributed to the success of this issue of POMACS. First, we would like to thank the authors, who submitted their best work to SIGMETRICS/POMACS. Second, we would like to thank the program committee members who provided constructive feedback in their reviews to authors and participated in the online discussions and program committee meeting. We also thank the several external reviewers who provided their expert opinion on specific submissions that required additional input. We are also grateful to the SIGMETRICS Board Chair, Giuliano Casale, and to past program committee Chairs, Niklas Carlsson, Edith Cohen, and Philippe Robert, who provided a wealth of information and guidance. Finally, we are grateful to the Organization Committee and to the SIGMETRICS Board for their ongoing efforts and initiatives for creating an exciting program for ACM SIGMETRICS 2023.

International audience; In this paper we consider a graph clustering problem with a given number of clusters and approximate desired sizes of the clusters. One possible motivation for such task could be the problem of databases or servers allocation within several given large computational clusters, where we want related objects to share the same cluster in order to minimize latency and transaction costs. This task differs from the original community detection problem. To solve this task, we adopt some ideas from Glauber Dynamics and Label Propagation Algorithm. At the same time we consider no additional information about node labels, so the task has the nature of unsupervised learning. We propose an algorithm for the problem, show that it works well for a large set of parameters of Stochastic Block Model (SBM) and theoretically show that its running time complexity for achieving almost exact recovery is of O(n·d·ω) for the mean-field SBM with d being the average degree and ω tending to infinity arbitrary slow. Other significant advantage of the proposed approach is its local nature, which means it can be efficiently distributed with no scheduling or synchronization.

International audience; This article studies the recovery of static communities in a temporal network. We introduce a temporal stochastic block model where dynamic interaction patterns between node pairs follow a Markov chain. We render this model versatile by adding degree correction parameters, describing the tendency of each node to start new interactions. We show that in some cases the likelihood of this model is approximated by the regularized modularity of a time-aggregated graph. This time aggregated graph involves a trade-off between new edges and persistent edges. A continuous relaxation reduces the regularized modularity maximization to a normalized spectral clustering. We illustrate by numerical experiments the importance of edge persistence, both on simulated and real data sets.

Discrete-time game-theoretic models of resource exploitation are treated as dynamic potential games. The players (countries or firms) exploit a common stock on the infinite time horizon. The main aim of the paper is to obtain a potential for the linear-quadratic games of this type. The class of games where a potential can be constructed as a quadratic form is identified. As an example, the dynamic game of bioresource management is considered and the potentials are constructed in the case of symmetric and asymmetric players.

A search engine maintains local copies of different web pages to provide quick search results. This local cache is kept up-to-date by a web crawler that frequently visits these different pages to track changes in them. Ideally, the local copy should be updated as soon as a page changes on the web. However, finite bandwidth availability and server restrictions limit how frequently different pages can be crawled. This brings forth the following optimization problem: maximize the freshness of the local cache subject to the crawling frequencies being within prescribed bounds. While tractable algorithms do exist to solve this problem, these either assume the knowledge of exact page change rates or use inefficient methods such as MLE for estimating the same. We address this issue here. We provide three novel schemes for online estimation of page change rates, all of which have extremely low running times per iteration. The first is based on the law of large numbers and the second on stochastic approximation. The third is an extension of the second and includes a heavy-ball momentum term. All these schemes only need partial information about the page change process, i.e., they only need to know if the page has changed or not since the last crawled instance. Our main theoretical results concern asymptotic convergence and convergence rates of these three schemes. In fact, our work is the first to show convergence of the original stochastic heavy-ball method when neither the gradient nor the noise variance is uniformly bounded. We also provide some numerical experiments (based on real and synthetic data) to demonstrate the superiority of our proposed estimators over existing ones such as MLE. We emphasize that our algorithms are also readily applicable to the synchronization of databases and network inventory management., Comment: This is the author version of the paper accepted to {\it International Journal of Performance Evaluation}, Elsevier; 25 pages. arXiv admin note: text overlap with arXiv:2004.02167

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new L\'evy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy Flights into random walks on graphs and, as a result, allows both to accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs. Furthermore, we propose a new preferential P-DropEdge method based on the Girvan-Newman argument. That is, in contrast to uniform removing of edges as in DropEdge, following the Girvan-Newman algorithm, we detect network periphery structures using information on edge betweenness and then remove edges according to their betweenness centrality. Our experimental results on semi-supervised node classification tasks demonstrate that the LFGCN coupled with P-DropEdge accelerates the training task, increases stability and further improves predictive accuracy of learned graph topology structure. Finally, in our case studies we bring the machinery of LFGCN and other deep networks tools to analysis of power grid networks - the area where the utility of GDL remains untapped., Comment: To Appear in the 2020 IEEE International Conference on Data Mining (ICDM)

In this article, we analyze the limiting eigen-value distribution (LED) of random geometric graphs (RGGs). The RGG is constructed by uniformly distributing n nodes on the d-dimensional torus $\Gamma^{d}\equiv [0, 1]^{d}$ and connecting two nodes if their $\ell_{p}$-distance, $ p\in [1,\ \infty]$ is at most r n . In particular, we study the LED of the adjacency matrix of RGGs in the connectivity regime, in which the average vertex degree scales as $\log(n)$ or faster, i.e., $\Omega(\log(n))$. In the connectivity regime and under some conditions on the radius r n , we show that the LED of the adjacency matrix of RGGs converges to the LED of the adjacency matrix of a deterministic geometric graph (DGG) with nodes in a grid as n goes to infinity. Then, for n finite, we use the structure of the DGG to approximate the eigenvalues of the adjacency matrix of the RGG and provide an upper bound for the approximation error. Index Terms--Random geometric graphs, adjacency matrix, limiting eigenvalue distribution, Levy distance.

International audience; We consider the large graphs as the object of study and deal with the problem of escape probability estimation. Generally, the required characteristic cannot be calculated analytically and even numerically due to the complexity and large size of the investigation object. The purpose of this paper is to offer the effective method for estimating the probability that the random walk on graph first enters a node b before returning into starting node a. Regenerative properties of the random walk allow using an accelerated method for the cycles simulation based on the splitting technique. The results of numerical experiments confirm the advantages of the proposed method.

Network formation games have been proposed as a tool to explain the topological characteristics of existing networks. They assume that each node is an autonomous decision-maker, ignoring that in many cases different nodes are under the control of the same authority (e.g. an Autonomous System) and then they operate as a team. In this paper we introduce the concept of network formation games for teams of nodes and show how very different network structures can arise also for some simple games studied in the literature. Beside extending the usual definition of pairwise stable networks to this new setting, we define a more general concept of stability toward deviations from a specific set $\mathcal{C}$ of teams' coalitions ($\mathcal{C}$-stability). We study then a trembling-hand dynamics, where at each time a coalition of teams can create or sever links in order to reduce its cost, but it can also take wrong decisions with some small probability. We show that this stochastic dynamics selects $\mathcal{C}$-stable networks or networks from closed cycles in the long run as the error probability vanishes.

International audience; The betweenness centrality is one of the basic concepts in the analysis of the social networks. Initial definition for the betweenness of a node in the graph is based on the fraction of the number of geodesics (shortest paths) between any two nodes that given node lies on, to the total number of the shortest paths connecting these nodes. This method has polynomial complexity. We propose a new concept of the betweenness centrality for weighted graphs using the methods of cooperative game theory. The characteristic function is determined by special way for different coalitions (subsets of the graph). Two approaches are used to determine the characteristic function. In the first approach the characteristic function is determined via the number of direct and indirect weighted connecting paths in the coalition. In the second approach the coalition is considered as an electric network and the characteristic function is determined as a total current in this network. We use the Kirchhoff's law. After that the betweenness centrality is determined as the Myerson value. The results of computer simulations for some examples of networks, in particular, for the popular social network "VKontakte", as well as the comparing with the PageRank method are presented.

This book constitutes the refereed proceedings of the 8th EAI International Conference on Game Theory for Networks, GameNets 2019, held in Paris, France, in April 2019. The 8 full and 3 short papers presented were carefully reviewed and selected from 17 submissions. They are organized in the following topical sections: Game Theory for Wireless Networks; Games for Economy and Resource Allocation; and Game Theory for Social Networks.

International audience; Network geometries are typically characterized by having a finite spectral dimension (SD), that characterizes the return time distribution of a random walk on a graph. The main purpose of this work is to determine the SD of a variety of random graphs called random geometric graphs (RGGs) in the thermodynamic regime, in which the average vertex degree is constant. The spectral dimension depends on the eigenvalue density (ED) of the RGG normalized Laplacian in the neighborhood of the minimum eigenvalues. In fact, the behavior of the ED in such a neighborhood characterizes the random walk. Therefore, we first provide an analytical approximation for the eigenvalues of the regularized normalized Laplacian matrix of RGGs in the thermodynamic regime. Then, we show that the smallest non zero eigenvalue converges to zero in the large graph limit. Based on the analytical expression of the eigenvalues, we show that the eigenvalue distribution in a neighborhood of the minimum value follows a power-law tail. Using this result, we find that the SD of RGGs is approximated by the space dimension d in the thermodynamic regime.

International audience; We consider caching of VoD contents in a cellular network in which each base station is equipped with a cache. Videos are partitioned into chunks according to a layered coding mechanism and the goal is to place chunks in caches such that the expected utility is maximized. The utility depends on the quality at which a user is requesting a file and the chunks that are available. We impose alpha-fairness across files and qualities. We develop a distributed asynchronous algorithm for deciding which chunks to store in which cache.

International audience; We consider the Generalized Additive Increase Multiplicative Decrease (G-AIMD) dynamics for resource allocation with alpha fairness utility function. This dynamics has a number of important applications such as internet congestion control, charging electric vehicles, and smart grids. We prove indexability for the special case of MIMD model and provide an efficient scheme to compute the index. The use of index policy allows us to avoid the curse of dimensionality. We also demonstrate through simulations for another special case, AIMD, that the index policy is close to optimal and significantly outperforms a natural heuristic which penalizes the strongest user.

International audience; In this paper, we present some algebraic properties of a particular class of probability transition matrices, namely, Hamiltonian transition matrices. Each matrix P in this class corresponds to a Hamiltonian cycle in a given graph G on n nodes and to an irreducible, periodic, Markov chain. We show that a number of important matrices traditionally associated with Markov chains, namely, the stationary, fundamental, deviation and the hitting time matrix all have elegant expansions in the first n−1 powers of P , whose coefficients can be explicitly derived. We also consider the resolvent-like matrices associated with any given Hamiltonian cycle and its reverse cycle and prove an identity about the product of these matrices.

The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time.To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In this context, we propose a distributed algorithm that tackles the fair resource allocation problem in a distributed SDN control architecture. Our algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, we demonstrate that we can handle large instances in real-time.; La performance des réseaux informatiques est fortement liée au partage équitable de la bande-passante entre les différents flux.Lorsque la taille de ces flux varie constamment dans le temps, le problème de partage des ressources est non-trivial. Afin d'aborder ce problème, des techniques de partage pouvant réagir rapidement aux fluctuations de trafic sont désirables, en particulier pour le contrôle de grands réseaux avec des centaines de noeuds et des milliers de flux. Nous proposons un algorithme distribué qui s'attaque au problème de partage de ressources équitable dans le contexte des architectures Software-Defined Networks (SDN) distribuées. Cet algorithme génère en chaque instant des solutions convergeant vers le partage équitable en respectant toujours l'ensemble des contraintes, une propriété non satisfaite par les méthodes classiques de décomposition primale-duale. Grâce à la distribution des calculs, nous montrons que notre algorithme peut contrôler de grands réseaux en temps réel.

We describe a test statistic based on the L1-norm of the eigenvectors of a modularity matrix to detect the presence of an embedded Erdős Renyi (ER) subgraph inside a larger ER random graph. An embedded subgraph may model a hidden community in a large network such as a social network or a computer network. We make use of the properties of the asymptotic distribution of eigenvectors of random graphs to derive the distribution of the test statistic under certain conditions on the subgraph size and edge probabilities. We show that the distributions differ sufficiently for well defined ranges of subgraph sizes and edge probabilities of the background graph and the subgraph. This method can have applications where it is sufficient to know whether there is an anomaly in a given graph without the need to infer its location. The results we derive on the distribution of the components of the eigenvector may also be useful to detect the subgraph nodes.

We deal with zero-sum two-player stochastic games with perfect information. We propose two algorithms to find the uniform optimal strategies and one method to compute the optimality range of discount factors. We prove the convergence in finite time for one algorithm. The uniform optimal strategies are also optimal for the long run average criterion and, in transient games, for the undiscounted criterion as well.

Optimal control of stochastic bandwidth-sharing networks is typically difficult. In order to facilitate the analysis, deterministic analogues of stochastic bandwidth-sharing networks, the so-called fluid models, are often taken for analysis, as their optimal control can be found more easily. The tracking policy translates the fluid optimal control policy back to a control policy for the stochastic model, so that the fluid optimality can be achieved asymptotically when the stochastic model is scaled properly. In this work we study the efficiency of the tracking policy, that is, how fast the fluid optimality can be achieved in the stochastic model with respect to the scaling parameter. In particular, our result shows that, under certain conditions, the tracking policy can be as efficient as feedback policies.

The problem of jamming plays an important role in ensuring the quality and security of wireless communications, especially at this moment when wireless networks are quickly becoming ubiquitous. Since jamming can be considered as a game in which jammer is playing against the user (transmitter) who would like to transmit signal with good quality and at the same time with a reasonable amount of energy, game theory is an appropriate tool for dealing with jamming. Here we investigate the effect of partially available information and correlation among sub-carriers on the user behavior. Specifically, to do so we deal with the scenario when the user does not know how jamming efforts are distributed among sub-carriers and the user does not know the fading channels' gains with certainty. As an object function for the user we consider SINR. We consider zero-sum games, so all of them can also be viewed as a minimax problem for the user playing against the nature. We study independent fading channel gains scenario as well as dependent fading channel gains scenario, both in discrete and continuous versions. We show that in all the scenarii the jammers equalize the quality of the best sub-carriers for the transmitter on as low level as their power constraints allow. Meanwhile the transmitter distributes his power among these jamming sub-carriers. We find the equilibrium strategies in closed form and specify the range of sub-carriers where the transmitter can expect the jamming attack. Also, we show for independent plot these strategies depend only on the expected value of the transmitters channel gains meanwhile for the dependent plot they depend on the whole spectra of these gains. Thus, for independent plot the behaviour of the jammer is less fine tuned under environment since it works with the expected gains. The user for both scenarios has to take the whole spectra of the jamming gains but, of course, for the independent scenario he is less specific because of the jammer.

A random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was solved by the introduction of uniform random jumps with some probability. Up to the present, there is no final answer to the question about the choice of this probability. We propose to use a parameter-free centrality measure which is based on the notion of a quasi-stationary distribution. Specifically, we suggest four quasi-stationary based centrality measures, analyze them and conclude that they produce approximately the same ranking.

In this note we study multivariate perturbations of algebraic equations. In general, it is not possible to represent the perturbed solution as a Puiseux-type power series in a connected neighborhood. For the case of two perturbation parameters we provide a sufficient condition that guarantees such a representation. Then, we extend this result to the case of more than two perturbation parameters. We motivate our study by the perturbation analysis of a weighted random walk on the Web Graph. In an instance of the latter the stationary distribution of the weighted random walk, the so-called Weighted PageRank, may depend on two (or more) perturbation parameters in a manner that illustrates our theoretical development.

We consider systems of tandem blocking queues having a common retrial queue. The model represents dynamics of short TCP transfers in the Internet. Analytical results are available only for a specific example with two queues in tandem. We propose approximation procedures involving simple analytic expressions, based on mean value analysis (MVA) and on fixed point approach (FPA). The mean sojourn time of a job in the system and the mean number of visits to the orbit queue are estimated by the MVA which needs as an input the fractions of blocked jobs in the primary queues. The fractions of blocked jobs are estimated by FPA. Using a benchmark example of the system with two primary queues, we conclude that the approximation works well in the light traffic regime. We note that our approach becomes exact if the blocking probabilities are fixed. Finally, we consider two optimization problems regarding minimizing mean total sojourn time of a job in the system: (i) finding the best order of queues and (ii) allocating a given capacity among the primary queues.

We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) multi-socket congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. First, we show that trajectories always converge to limiting cycles. We characterize the cycles. Necessary and sufficient conditions for the absence of multiple jumps in the same cycle are obtained. Then, we propose an analytical framework for the optimal choice of the router buffer size. We formulate this problem as a multi-criteria optimization problem, in which the Lagrange function corresponds to a linear combination of the average goodput and the average delay in the queue. Our analytical results are confirmed by simulations performed with MATLAB Simulink.

We consider jamming in wireless networks in the framework of zero-sum games with α-utility functions. The base station has to distribute the power fairly among the users in the presence of a jammer. The jammer in turn tries to distribute its power among the channels to produce as much harm as possible. The Shannon capacity and SNIR optimization are particular cases of the proposed more general α-fairness SNIR based utility functions. Specifically, we consider two α-fairness utility functions, based on SNIR and Shifted SNIR. This game can also be viewed as a minimax problem against the nature. We show that the game has the unique equilibrium and investigate its properties. In particular, in several important cases we present the equilibrium strategies and the Jain's fairness index in closed form. It turns out that there is an important difference between SNIR and Shifted SNIR α-fairness utility functions. In the case of the SNIR based utility function all users obtain nonzero powers when α > 0. On contrary, when the Shifted SNIR based utility function is used, some users with bad channel conditions might not receive any power at all. We have also detected a surprising non-monotone behaviour of the Jain's fairness index in the case of the SNIR based utility function.

We study the interaction between the MIMD (Multiplicative Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. We study conditions under which the system trajectories converge to limiting cycles with a single jump. Following that, we consider the problem of the optimal buffer sizing in the framework of multi-criteria optimization in which the Lagrange function corresponds to a linear combination of the average throughput and the average delay in the queue. As case studies, we consider the Slow Start phase of TCP New Reno and Scalable TCP for high speed networks. © 2009 Elsevier B.V. All rights reserved.

We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. We consider two frameworks concerning the state information of the channels of other mobiles: i) the case of full state information and ii) the case of local state information. In each of the two frameworks, we consider both cooperative as well as non-cooperative power control. We manage to characterize the structure of equilibria policies and, more generally, of best-response policies in the non-cooperative case. We present an algorithm to compute equilibria policies in the case of two non-cooperative players. Finally, we study the case where a malicious mobile, which also has average power constraints, tries to jam the communication of another mobile. Our results are illustrated and validated through various numerical examples.

International audience; We propose two asynchronously distributed approaches for graph-based semi-supervised learning. The first approach is based on stochastic approximation, whereas the second approach is based on randomized Kaczmarz algorithm. In addition to the possibility of distributed implementation, both approaches can be naturally applied online to streaming data. We analyse both approaches theoretically and by experiments. It appears that there is no clear winner and we provide indications about cases of superiority for each approach.

International audience; Linear programming formulations for the discounted and long-run average MDPs have evolved along separate trajectories. In 2006, E. Altman conjectured that the two linear programming formulations of discounted and long-run average MDPs are, most likely, a manifestation of general properties of singularly perturbed linear programs. In this note we demonstrate that this is, indeed, the case.

International audience; We consider pairwise Markov random fields which have a number of important applications in statistical physics, image processing and machine learning such as Ising model and labeling problem to name a couple. Our own motivation comes from the need to produce synthetic models for social networks with attributes. First, we give conditions for rapid mixing of the associated Glauber dynamics and consider interesting particular cases. Then, for pairwise Markov random fields with submodular energy functions we construct monotone perfect simulation.

Consider the nonpreemptive priority queueing system with two classes of packets. Class-1 packets have priority over class-2 packets. The packets of class 1 (2) arrive into the buffer according to the Poisson process with rate λ1 (λ2), respectively. The service time has the exponential distribution with the same rate μ for each class. The service times are independent of the arrival processes. The buffer has a finite size N and it is shared by both types of customers. If the buffer is full, a new incoming customer of class 1 can push out of the buffer a customer of class 2 with probability α. Note that if α = 1, we retrieve the standard nonrandomized push-out mechanism. The infinite buffer priority queueing has been thoroughly studied in [4, 7, 8]. The case of finite buffer priority queueing has received considerably less attention. The M | M | C | K type finite-buffer nonpreemptive priority queueing with nonrandomized push-out mechanism is analyzed in [5, 6]. Bondi, in [1], considers the M | M | 1 | K type preemptive and nonpreemptive priority queueing with the following buffer management schemes: complete partitioning, complete sharing, and sharing with minimum allocation. Wagner and Krieger, in [9], analyze the M | M | 1 | K type nonpreemptive priority queueing with complete sharing buffer management scheme and with class-dependent service rates. In [2], Cheng and Akyildiz consider the priority queueing with general service-time distributions and a general service discipline function. Most of the above works use recursive relations to solve steady-state Kolmogorov equations. We use a generating function approach, which only requires the solution of a linear system ofN equations. As far as we know, the randomized push-out mechanism is analyzed for the first time.

The Discriminatory Processor Sharing (DPS) model is a multi-class generalization of the egalitarian Processor Sharing model. In the DPS model all jobs present in the system are served simultaneously at rates controlled by a vector of weights {gk > 0; k = 1,..., K }. If there are Nk jobs of class k present in the system, k = 1,..., K, each class-k job is served at rate $$g_k/\sum_{j=1}^K{g_j}{N_j}$$ . The present article provides an overview of the analytical results for the DPS model. In particular, we focus on response times and numbers of jobs in the system.

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints

We analyze a Processor-Sharing queue with Batch arrivals. Our analysis is based on the integral equation derived by Kleinrock, Muntz and Rodemich. Using the contraction mapping principle, we demonstrate the existence and uniqueness of a solution to the integral equation. Then we provide asymptotical analysis as well as tight bounds for the expected response time conditioned on the service time. In particular, the asymptotics for large service times depends only on the first moment of the service time distribution and on the first two moments of the batch size distribution. That is, similarly to the Processor-Sharing queue with single arrivals, in the Processor-Sharing queue with batch arrivals the expected conditional response time is finite even when the service time distribution has infinite second moment. Finally, we show how the present results can be applied to the Multi-Level Processor-Sharing scheduling.