Research Interests and Selected Publications:


Network Science

Recently, a new inter-disciplinary research initiative has emerged. This initiative is referred to as "Network Science" or "Complex Network Analysis". It aims at understanding the structural properties and the dynamics of various kind of large scale networks in telecommunication (e.g., the Internet, the web graph, peer-to-peer networks), social science (e.g., community of interest, advertisement, recommendation systems), bibliometrics (e.g., citations, co-authors), biology (e.g., spread of an epidemic, protein-protein interactions), and physics. The complex networks encountered in these areas share common properties such as power law degree distribution, small average distances, community structure, etc. It also appears that many general questions/applications (centrality measures, e.g., PageRank, community detection, epidemic spreading, search, anomaly detection) are common in various disciplines which study networks.

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Game Theory and its Applications

In Game Theory I am mostly interested in Markovian Competitive Decision Processes (Stochastic Games), games with constraints and formation games. These types of games find applications in wireless network power control, routing and network formation.

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Performance Evaluation and Optimization of Computer Networks

In the Internet the reliable file transfer is done with the help of TCP/IP protocol. For instance, Web browsing and FTP applications are based on TCP. We are interested in the performance evaluation and optimization of the TCP/IP computer networks in terms of packet losses, packet delays, throughputs and latencies of file transfers.

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Theory of Singular and Analytic Perturbations

Analytic perturbation theory deals with a wide spectrum of mathematical problems (e.g., the inversion of linear operators, the eigenvalue problems, the systems of linear and nonlinear equations, mathematical programming) whose data depend analytically on a "small" perturbation parameter. There are at least two motivations to study this class of problems. Firstly, it is often necessary to describe the behaviour of a problem solution with respect to the change of its parameters. Secondly, admitting that we never have precise data, it is of great importance to analyse the influence of data perturbations. Sometimes even small perturbations of the data cause dramatic changes in the properties of the problem. The latter case is called the singular perturbation and it is of particular interest for our research.

Ph.D. Thesis:

Book:

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Singularly Perturbed Markov Chains and Decision Processes

Here we apply the results of the general analytic perturbation theory to singularly perturbed Markov chains and Markov decision processes. The singularly perturbed Markov chain is an appropriate model for a complex stochastic system which consists of several weakly connected subsystems.

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Queueing Theory

One can still obtain new interesting results for classical queueing models! In particular, I am interested in processor sharing queues, retrial queues, stochastic scheduling, multi-class queues and their applications in communication systems.

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Iterative Learning Control

Iterative learning control (ILC) is designed to improve the performance of a cyclic system. The basic idea of ILC is to correct the control input for the next cycle using the information about the error from the current and previous cycles. If the unknown part of the system can be represented as a regular perturbation, then we propose to use fast convergent quasi-Newton-type methods. However, if the unknown part of the system is a singular perturbation, then we recommend to use robust methods based on H-infinity controller design.

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Miscellaneous

Here is a collection of cute results that cannot be classified into any of the above topics.

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