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Papers by Konstantin Avrachenkov

Abstract: We analyze with NS simulations the aggregated packet arrival process into a bottleneck ... 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 ...

ArXiv, 2015

Online social networks (OSN) contain extensive amount of information about the underlying society... 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.

The ANZIAM Journal, 2020

The population dynamics for the replicator equation has been well studied in continuous time, but... 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.

We describe a systematic procedure to calculate the resolvent operator for a linear pencil on Ban... 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.

2019 24th Conference of Open Innovations Association (FRUCT), 2019

2016 IEEE 55th Conference on Decision and Control (CDC), Dec 1, 2016

2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Jul 1, 2019

2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), 2015

Applied Optimization, 2001

ABSTRACT

Lecture Notes in Computer Science, 2004

Radio resources management in WiMAX: from theoretical capacity to system simulations, 2009

The first version of WiMAX, for fixed broadband access in the 10-66 Ghz range, was started in 199... 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.

We explore the dependence structure in the sampled sequence of large networks. We consider random... 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.

In this paper, we address the problem of quick detection of high-degree entities in large online ... 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...

We analyze a Processor-Sharing queue with Batch arrivals. Our analysis is based on the integral e... 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.