Konstantin Avrachenkov
INRIA, Inria Sophia Antipolis-Méditerranée, Faculty Member
Abstract: We analyze with NS simulations the aggregated packet arrival process into a bottleneck queue generated by multiplexed TCP flows. We explain qualitatively the shape of the packet interarrival time distribution. In particular, we... more
Abstract: We analyze with NS simulations the aggregated packet arrival process into a bottleneck queue generated by multiplexed TCP flows. We explain qualitatively the shape of the packet interarrival time distribution. In particular, we provide conditions under which the distribution of the inter packet arrivals is close to exponential and show how this condition scales when the network capacity becomes large. In addition, we analyze the structure of the autocorrelation function of times between packet arrivals. For the case of a packet arrival ...
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Online social networks (OSN) contain extensive amount of information about the underlying society that is yet to be explored. One of the most feasible technique to fetch information from OSN, crawling through Application Programming... more
Online social networks (OSN) contain extensive amount of information about the underlying society that is yet to be explored. One of the most feasible technique to fetch information from OSN, crawling through Application Programming Interface (API) requests, poses serious concerns over the the guarantees of the estimates. In this work, we focus on making reliable statistical inference with limited API crawls. Based on regenerative properties of the random walks, we propose an unbiased estimator for the aggregated sum of functions over edges and proved the connection between variance of the estimator and spectral gap. In order to facilitate Bayesian inference on the true value of the estimator, we derive the asymptotic posterior distribution of the estimate. Later the proposed ideas are validated with numerical experiments on inference problems in real-world networks.
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The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by... more
The population dynamics for the replicator equation has been well studied in continuous time, but there is less work that explicitly considers the evolution in discrete time. The discrete-time dynamics can often be justified indirectly by establishing the relevant evolutionary dynamics for the corresponding continuous-time system, and then appealing to an appropriate approximation property. In this paper we study the discrete-time system directly, and establish basic stability results for the evolution of a population defined by a positive definite system matrix, where the population is disrupted by random perturbations to the genotype distribution either through migration or mutation, in each successive generation.
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We describe a systematic procedure to calculate the resolvent operator for a linear pencil on Banach space and thereby simplify, unify and extend known methods for resolution and representation of marginally stable time series. We pay... more
We describe a systematic procedure to calculate the resolvent operator for a linear pencil on Banach space and thereby simplify, unify and extend known methods for resolution and representation of marginally stable time series. We pay particular attention to those time series commonly known as unit root processes. The new method uses infinite-length Jordan chains to find the key spectral separation projections which enable separation and solution of the fundamental equations for the Laurent series coefficients of the resolvent. It is then possible to define the desired Granger-Johansen representation for the time series. The method remains valid when the resolvent has an isolated essential singularity at unity.
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ABSTRACT
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The first version of WiMAX, for fixed broadband access in the 10-66 Ghz range, was started in 1998 and was completed in October 2001. It was amended in version 802.16 a to behind 2-11 GHz in January 2001. Version 802.16 d, completed in... more
The first version of WiMAX, for fixed broadband access in the 10-66 Ghz range, was started in 1998 and was completed in October 2001. It was amended in version 802.16 a to behind 2-11 GHz in January 2001. Version 802.16 d, completed in January 2004, brings some enhancements in the uplink. Version 802.16 e is mainly about mobility and asymmetric links.
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We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like... more
We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers or income of the nodes in Online Social Networks etc, which satisfy two mixing conditions. Several useful extremes of the sampled sequence like kth largest value, clusters of exceedances over a threshold, first hitting time of a large value etc are investigated. We abstract the dependence and the statistics of extremes into a single parameter that appears in Extreme Value Theory, called extremal index (EI). In this work, we derive this parameter analytically and also estimate it empirically. We propose the use of EI as a parameter to compare different sampling procedures. As a specific example, degree correlations between neighboring nodes are studied in detail with three prominent random walks as sampling techniques.
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In this paper, we address the problem of quick detection of high-degree entities in large online social networks. Practical importance of this problem is attested by a large number of companies that continuously collect and update... more
In this paper, we address the problem of quick detection of high-degree entities in large online social networks. Practical importance of this problem is attested by a large number of companies that continuously collect and update statistics about popular entities, usually using the degree of an entity as an approximation of its popularity. We suggest a simple, efficient, and easy to implement two-stage randomized algorithm that provides highly accurate solutions for this problem. For instance, our algorithm needs only one thousand API requests in order to find the top-100 most followed users in Twitter, a network with approximately a billion of registered users, with more than 90% precision. Our algorithm significantly outperforms existing methods and serves many different purposes, such as finding the most popular users or the most popular interest groups in social networks. An important contribution of this work is the analysis of the proposed algorithm using Extreme Value Theory...
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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... more
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 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.
Research Interests: Mathematics, Applied Mathematics, Computer Science, Statistics, asymptotic Analysis, and 9 moreSize Distribution, Time Dependent, Queueing Systems, Numerical Analysis and Computational Mathematics, Conservation of Metallic Art Work, Integral Equation, Batch arrival, Processor Sharing, and Existence and uniqueness
We compare the performance of Cubic, Compound TCP, HighSpeed TCP and Reno under a simple loss model, where each packet is dropped with probability p. Modeling the evolution of the congestion window with a Markov chain, we can use... more
We compare the performance of Cubic, Compound TCP, HighSpeed TCP and Reno under a simple loss model, where each packet is dropped with probability p. Modeling the evolution of the congestion window with a Markov chain, we can use efficient numerical algorithms to compute the average window size (response function), the Coefficient of Variation (CoV) of the window and the average throughput. We find that, for smaller bandwidth delay products, Cubic can have a similar throughput to Reno while for larger values the throughput of all new versions is similar and larger than Reno. The CoV of Cubic has a peak but it is otherwise the smallest one. This peak corresponds with a sharp increase in the response function.
We consider a dynamic multiagent system in which several states succeed each other, following a Markov chain process. In each state, a different single stage game among the agents, or players, is played, and cooperation among subsets of... more
We consider a dynamic multiagent system in which several states succeed each other, following a Markov chain process. In each state, a different single stage game among the agents, or players, is played, and cooperation among subsets of players can arise in order to achieve a common goal. We assume that each coalition can ensure a certain value for itself. The Shapley value is a well known method to share the value of the grand coalition, formed by all the players, among the players themselves. It reflects the effective incremental asset brought by each player to the community. Unfortunately, the exact computation of the Shapley value for each player requires an exponential complexity in the number of players. Moreover, we prove that an exponential number of queries is necessary for any deterministic algorithm even to approximate the Shapley value in a Markovian dynamic game with polynomial accuracy. Motivated by these reasons, we propose three different methods to compute a confide...
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We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. First, we... more
We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) 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 the hybrid model of the interaction between the AIMD congestion control and bottleneck router always converges to a cyclic behavior. We characterize the cycles. Necessary and sufficient conditions for the absence of multiple jumps of congestion window in the same cycle are obtained. Then, we propose an analytical framework for the optimal choice of the router buffer size. We formulate the problem of the optimal router buffer size 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. The solution to the optimization problem provides further evidence that the buffer size should be reduced in the presence of traffic aggregation. Our ...
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The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting denser subgraphs inside the network. Here we propose to use the methods... more
The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting denser subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolution. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity based approach and its generalizations can be viewed as particular cases of the hedonic games.
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This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired... more
This paper studies iterative learning control (ILC) for under-determined and over-determined systems, i.e., systems for which the control action to produce the desired output is not unique, or for which exact tracking of the desired trajectory is not feasible. For both cases we recommend the use of the pseudoinverse or its approximation as a learning operator. The Tikhonov regularization technique is discussed for computing the pseudoinverse to handle numerical instability. It is shown that for over-determined systems, the minimum error is never reached by a repetition invariant learning controller unless one knows the system exactly. For discrete time uniquely determined systems it is indicated that the inverse is usually ill-conditioned, and hence an approximate inverse based on a pseudoinverse is appropriate, treating the system as overdetermined. Using the structure of the system matrix, an enhanced Tikhonov regularization technique is developed which converges to zero tracking ...
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We consider wireless caches located in the plane according to general point process and specialize the results for the homogeneous Poisson process. A large data file is stored at the caches, which have limited storage capabilities. Hence,... more
We consider wireless caches located in the plane according to general point process and specialize the results for the homogeneous Poisson process. A large data file is stored at the caches, which have limited storage capabilities. Hence, they can only store parts of the data. Clients can contact the caches to retrieve the data. We compare the expected cost of obtaining the complete data under uncoded as well as coded data allocation strategies. It is shown that for the general class of cost measures where the cost of retrieving data is increasing with the distance between client and caches, coded allocation outperforms uncoded allocation. The improvement offered by coding is quantified for two more specific classes of performance measures. Finally, our results are validated by computing the costs of the allocation strategies for the case that caches coincide with currently deployed mobile base stations.
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We study the impact of the modifications proposed for TCP in the context of short file transfers. The two most important proposals are the increment of the initial window size (IW) [3] and the Limited Transmit algorithm (LT) [1]. We... more
We study the impact of the modifications proposed for TCP in the context of short file transfers. The two most important proposals are the increment of the initial window size (IW) [3] and the Limited Transmit algorithm (LT) [1]. We analyze analytically and by simulations the effect of these proposals on the TCP latency. We demonstrate that the LT proposal reduces the TCP latency similarly to the IW proposal however LT is less aggressive than IW. Nevertheless, in the context of short file transfers we point out a scenario, when upon a single packet loss the sender times out even if IW or LT are enabled. This harmful scenario happens when the very last packets of the file transfer are lost. Therefore to avoid this situation we propose a new modification which is based on reducing the number of duplicate acknowledgements TCP reacts to. In order to avoid the potentially harmful effect of needless retransmissions on the network load we suggest to implement the new modification only for ...
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In this paper we apply the Gittins optimality result to characterize the optimal scheduling discipline in a multi-class M/G/1 queue. We apply the general result to several cases of practical interest where the service time distributions... more
In this paper we apply the Gittins optimality result to characterize the optimal scheduling discipline in a multi-class M/G/1 queue. We apply the general result to several cases of practical interest where the service time distributions belong to the set of decreasing hazard rate distributions, like Pareto or hyper-exponential. When there is only one class it is known that in this case the Least Attained Service policy is optimal. We show that in the multi-class case the optimal policy is a priority discipline, where jobs of the various classes depending on their attained service are classified into several priority levels. Using a tagged-job approach we obtain, for every class, the mean conditional sojourn time. This allows us to compare numerically the mean sojourn time in the system between the Gittins optimal and popular policies like Processor Sharing, First Come First Serve and Least Attained Service (LAS). We implement the Gittins' optimal algorithm in NS-2 and we perform...
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We study a problem of quick detection of top-k Personalized PageRank lists. This problem has a number of important applications such as finding local cuts in large graphs, estimation of similarity distance and name disambiguation. In... more
We study a problem of quick detection of top-k Personalized PageRank lists. This problem has a number of important applications such as finding local cuts in large graphs, estimation of similarity distance and name disambiguation. In particular, we apply our results to construct efficient algorithms for the person name disambiguation problem. We argue that when finding top-k Personalized PageRank lists two observations are important. Firstly, it is crucial that we detect fast the top-k most important neighbours of a node, while the exact order in the top-k list as well as the exact values of PageRank are by far not so crucial. Secondly, a little number of wrong elements in top-k lists do not really degrade the quality of top-k lists, but it can lead to significant computational saving. Based on these two key observations we propose Monte Carlo methods for fast detection of top-k Personalized PageRank lists. We provide performance evaluation of the proposed methods and supply stopping criteria. Then, we apply the methods to the person name disambiguation problem. The developed algorithm for the person name disambiguation problem has achieved the second place in the WePS 2010 competition.
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A method for packet flow rate control within a network node (4) receiving at least a traffic flow from a sender (1), comprising the following steps: - computing the average rate at the end of a cycle comprising an initial value of packet... more
A method for packet flow rate control within a network node (4) receiving at least a traffic flow from a sender (1), comprising the following steps: - computing the average rate at the end of a cycle comprising an initial value of packet number; - updating the value of packet number per cycle in function of the computed average rate with respect to a target flow rate.
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Research Interests: Mathematics, Applied Mathematics, Computer Science, Statistics, asymptotic Analysis, and 9 moreSize Distribution, Time Dependent, Queueing Systems, Numerical Analysis and Computational Mathematics, Conservation of Metallic Art Work, Integral Equation, Batch arrival, Processor Sharing, and Existence and uniqueness
Data on the Internet is sent by packets that go through a network of routers. A router drops packets either when its buffer is full or when it uses the Active Queue Management. Currently, the majority of the Internet routers use a simple... more
Data on the Internet is sent by packets that go through a network of routers. A router drops packets either when its buffer is full or when it uses the Active Queue Management. Currently, the majority of the Internet routers use a simple Drop Tail strategy. The rate at which a user injects the data into the network is determined by transmission control protocol (TCP). However, most connections in the Internet consist only of few packets, and TCP does not really have an opportunity to adjust the sending rate. Thus, the data flow generated by short TCP connections appears to be some uncontrolled stochastic process. In the present work we try to describe the interaction of the data flow generated by short TCP connections with a network of finite buffers. The framework of retrial queues and networks seems to be an adequate approach for this problem. The effect of packet retransmission becomes essential when the network congestion level is high. We consider several benchmark retrial netw...