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Tomsk state university

Institute of Applied Mathematics and Computer Science



Queueing theory and probabilistic methods


Development of mathematical methods and models for communication networks and distributed data processing systems analysis. Problems of mathematical teletraffic theory and queuing theory.

Research Group on queueing theory and probabilistic methods for communication networks, Tomsk State University

We have about 25 researchers involved in the studies devoted to application of mathematical modeling and methods for solving problems in various fields, including communication networks. In our studies, we mainly use applied probability analysis, queueing theory and simulations. Our research group is the biggest in Russia in the field of queueing theory and well-known among queueing theory specialists around the world.

Leading researchers:


NazarovAA.jpg Anatoly Nazarov (1947) – Professor, Doctor in Engineering, Full Professor at the Department of Probability and Statistics of Tomsk State University. He has published 8 books and about 550 papers, including 146 indexed by Scopus and Wеb of Science (Scopus h-index = 10).
SP_SU.png Sergey Suschenko (1952) – Professor, Doctor in Engineering, Head of the Department of Applied Informatics of Tomsk State University. He has published 6 books and about 280 papers, including 27 indexed by Scopus and Wеb of Science (Scopus h-index = 3).
61649-Full.png Svetlana Moiseeva (1971) – Professor, Doctor in Mathematics and Physics, Full Professor at the Department of Probability and Statistics of Tomsk State University. She has published 7 books and about 200 papers, including 39 indexed by Scopus and Wеb of Science (Scopus h-index = 6).
28959-Full.jpg.png Alexander Moiseev (1971) – Doctor in Mathematics and Physics, Head of the Department of Software Engineering of Tomsk State University. He has published 2 books and about 180 papers, including 41 indexed by Scopus and Wеb of Science (Scopus h-index = 8).

Our group is engaged in developing mathematical models for various real systems and processes in communications and distributed data processing, and also applying known techniques and developing new methods for the model’s investigation.

Main skills, developed methods and results:


  • mathematical models of communication networks and distributed data processing systems in forms of queueing systems and networks of different types and configurations, including classic queues with a single server or limited number of servers, infinite-server queues, retrial queues, multi-stage (multi-phase) queueing systems including systems with feedback, combining simple buffers and orbits, system with collisions, priorities, outgoing calls, impatient customers, resource queueing systems, queues in a random environment, queueing networks, etc., including both Markovian and non-Markovian models;
  • modeling of computer networks at various architectural levels including wireless level networks access, including models of procedures for managing an individual data link transmission and a multilink transport connection that takes into account the distortion factors in communication channels and blocking of the buffer memory of transit switching nodes, as well as the level of the load on network connections and the pipeline effect that manifests itself when multi-packets messages are transported over multi-link data paths, analysis in applicability of forward error correction technique;
  • developed authors’ methods: dynamic screening method for study of non-Markovian queueing models with infinite number of servers; method of limiting decomposition for study infinite-server models with Poisson arrivals; method of asymptotic analysis which is used to find a solution when ‘classical’ methods do not work; and several original methods for analysis of systems with finite number of servers and a buffer;
  • methods for calculating the operational characteristics of network topological structures and optimizing protocol parameters and the structure of data transmission paths, methods for preventing the effect of capturing the wireless data transmission medium.

Our group organizes annual International Scientific Conference “Information Technologies and Mathematical Modelling”. The most significant session involving many scientists and researchers is about queueing theory and applications. Selected revised papers from this session are annually published in the special volume of Communication in Computer and Information Science series (Springer Verlag). You may find details on the conference website: http://itmmconf.ru

Projects implemented by the group:


  • Analytical Federal Program “Developing of High School Potential 2009-2011”.
  • Federal Programs «Research and Pedagogical staff for innovative Russia», 2009-2013, topic “Developing of Complex for Monitoring on Atmosphere and Prediction of Dangerous Weather Phenomenon nearby Airports Using Local Observation and High-Definition Models”.
  • Program of Ministry of Education and Science of Russia, 2012-2013, topic “Developing and Analyzing Probabilistic, Statistical and Logical Models of Components of Integrated Information Communication Networks of Information Processing, Storage, Transmission and Security”.
  • Program of Ministry of Education and Science of Russia, 2014-2016, topic “Analysis of Mathematical Models of Information Flows, Computer Networks, Algorithms of Information Processing and Transmissions”.
  • Program of Ministry of Education and Science of Russia, 2017, topic “Basic Methodology of Constructing of Software-Hardware Systems for Multidimensional Visualization in Problems of Observing and Control”.
  • Series of projects in collaboration with Incom company (2012-2017).
  • A project in collaboration with SberBank (2014).


Recent significant papers:


  1. Nazarov, A., Farkhadov, M., Gelenbe, E. Markov and non-Markov probabilistic models of interacting flows of annihilating particles (2016) Communications in Computer and Information Science, 638, pp. 281-291. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84986226561&doi=10.1...
  2. Nazarov A., Moiseev A. Queueing network MAP – (GI|∞)K with high-rate arrivals // European Journal of Operation Research – 2016. V. 254. P. 161-168 http://www.sciencedirect.com/science/article/pii/S037722171630230
  3. Ivnitskii, V., Moiseev, A. New results for a thinned renewal process (2016) Communications in Computer and Information Science, 638, pp. 132-139. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84986188624&doi=10.1...
  4. Melikov, A., Zadiranova, L., Moiseev, A. Two asymptotic conditions in queue with MMPP arrivals and feedback (2016) Communications in Computer and Information Science, 678, pp. 231-240. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85013432448&doi=10.1...
  5. Kokshenev, V.V., Mikheev, P.A., Sushchenko, S.P. Comparative analysis of the performance of selective and group repeat transmission modes in a transport protocol. Automation and Remote Control, Volume 78, Issue 2, 2017, pp. 247-260. https://link.springer.com/article/10.1134/S0005117917020059
  6. Nazarov, A., Broner, V. Inventory management system with on/off control of output product flow (2017) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10684 LNCS, pp. 132-144. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039454910&doi=10.1...
  7. Dudin, A., Nazarov, A. On a tandem queue with retrials and losses and state dependent arrival, service and retrial rates (2017) International Journal of Operational Research, 29 (2), pp. 170-182. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85019150551&doi=10.1...
  8. Nazarov, A., Paul, S., Gudkova, I. Asymptotic analysis of Markovian retrial queue with two-way communication under low rate of retrials condition (2017) Proceedings - 31st European Conference on Modelling and Simulation, ECMS 2017, pp. 687-693.  https://www.scopus.com/inward/record.uri?eid=2-s2.0-85021804546&partnerI...
  9. Bérczes, T., Sztrik, J., Tóth, Á., Nazarov, A. Performance modeling of finite-source retrial queueing systems with collisions and non-reliable server using MOSEL (2017) Communications in Computer and Information Science, 700, pp. 248-258.  https://www.scopus.com/inward/record.uri?eid=2-s2.0-85029677438&doi=10.1...
  10. Burtovaya, D., Demin, A., Demeshko, M., Moiseev, A., Kudryashova, A. Simulation of the communication system between an AUV group and a surface station (2017) Journal of Physics: Conference Series, 803 (1), paper no. 012027.  https://www.scopus.com/inward/record.uri?eid=2-s2.0-85018769902&doi=10.1...
  11. Danilyuk, E.Y., Fedorova, E.A., Moiseeva, S.P. Asymptotic Analysis of an Retrial Queueing System M|M|1 with Collisions and Impatient Calls (2018) Automation and Remote Control, 79 (12), pp. 2136-2146.https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058290122&doi=10.1134%2fS0005117918120044&partnerID=40&md5=9966b42e92909c168bd681f843c5d7a8
  12. Rozhkova, S.V., Rozhkova, V.I., Moiseeva, S.P., Pagano, M. Recognition of Stochastic System States for Continuous-Discrete Observations with Sliding Memory (2018) Russian Physics Journal, 61 (3), pp. 595-601. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85049693267&doi=10.1007%2fs11182-018-1438-y&partnerID=40&md5=26bae2c778c003888cb4e89e7b43f8e2
  13. Vygovskaya, O., Danilyuk, E., Moiseeva, S. Retrial Queueing System of MMPP/M/2 Type with Impatient Calls in the Orbit (2018) Communications in Computer and Information Science, 912, pp. 387-399. DOI: 10.1007/978-3-319-97595-5_30 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053181201&doi=10.1007%2f978-3-319-97595-5_30&partnerID=40&md5=49cc1beaa8eccee3f4df15ef87f4b425
  14. Mikheev, P., Pichugina, A., Suschenko, S. Modeling of a Multi-link Transport Connection by a Network of Queuing Systems (2018) Communications in Computer and Information Science, 912, pp. 274-289. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053186330&doi=10.1...
  15. Bogushevsky, D., Mikheev, P., Pristupa, P., Suschenko, S. The time-out length influence on the available bandwidth of the selective failure mode of transport protocol in the load data transmission path (2018) Communications in Computer and Information Science, 919, pp. 120-131. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053898607&doi=10.1...
  16. Nazarov, A., Sztrik, J., Kvach, A., Bérczes, T. Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs (2019) Annals of Operations Research, 277 (2), pp. 213-229. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053909422&doi=10.1...
  17. Nazarov, A., Phung-Duc, T., Paul, S. Slow Retrial Asymptotics for a Single Server Queue with Two-Way Communication and Markov Modulated Poisson Input (2019) Journal of Systems Science and Systems Engineering, 28 (2), pp. 181-193. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85061596213&doi=10.1...
  18. Shklennik, M.A., Moiseev, A.N. Mathematical Model of a System for Physics Experimental Data Processing with the Need to Reprocess Data (2019) Russian Physics Journal, 62 (3), pp. 553-560. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068908302&doi=10.1...
  19. Lisovskaya, E.Y., Moiseev, A.N., Moiseeva, S.P., Pagano, M. Modeling of Mathematical Processing of Physics Experimental Data in the Form of a Non-Markovian Multi-Resource Queuing System (2019) Russian Physics Journal, 61 (12), pp. 2188-2196. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85066490784&doi=10.1...
  20. Pankratova, E.V., Moiseeva, S.P., Farhadov, M.P., Moiseev, A. Heterogeneous system MMPP/GI(2)/∞ with random customers capacities (2019) Journal of Siberian Federal University - Mathematics and Physics, 12 (2), pp. 231-239. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85067016011&doi=10.1....


Applied probabilistic analysis of complex systems


Fundamental-academic research in the field of applied probabilistic analysis of complex systems, creation of methods of nonparametric statistics and identification of dynamic systems, as well as methods of mathematical modeling;



  • 01.01.2015 — 31.12.2015  Development of social technologies of public administration based on the state analysis of modern Russian society in innovative territories, taking into account global integration processes. State support of the leading universities of Russian Federation in order to improve their competitiveness among the world's leading research and educational centers (5-100)
  • 01.01.2015 — 31.12.2016

Modern adaptation of robust statistics and quantitative finance methods and their applications
State support of the leading universities of  Russian Federation in order to improve their competitiveness among the world's leading research and educational centers (5-100)

  • 14.04.2017 — 31.12.2017 

Factors of development of female entrepreneurship in the context of the “service” model of public administration in Russian Federation
State support of the leading universities of Russian Federation in order to improve their competitiveness among the world's leading research and educational centers (5-100)

  •  19.03.2018 — 31.12.2018 

Current models and calculations in social insurance systems State support of the leading universities of Russian Federation in order to improve their competitiveness among the world's leading research and educational centers (5-100)

  • 04.05.2017 — 31.12.2019

New robust efficient statistical methods for processing signals and images in stochastic systems

  •   19.03.2018 — 31.12.2018

Efficient and robust methods for identification of dynamic stochastic systems under various a priori uncertainty
State support of the leading universities of Russian Federation in order to improve their competitiveness among the world's leading research and educational centers (5-100)

Recent significant papers:


  1. Vavilov V.P., Koshkin G.M., Udod V.A., Fofanov O.B. Analytical Approximation of Spectrum for Pulse X-ray Tubes //JPCS. 2016. Vol. 671. P. 012061.          
  2. Gennady Koshkin, Valery Smagin. Kalman Filtering and Forecasting Algorithms with Use of Nonparametric Functional Estimators //Springer Proceedings in Mathematics & Statistics. 2016. Vol. 175: Nonparametric Statistics. P. 75-84.           
  3. Danchenko, MA, Kabanova, TV, Kabanova, SA, Zenkova, Zh.N. The influence of technogenic and climatic factors on the state of forest plantations of the sanitary protection zone of Tomskneftekhim LLC // New technologies. 2018. No. 3. Pp. 187-195.
  4. Konev V.V., Nazarenko B.N. Sequential fixed accuracy estimation for nonstationary autoregressive processes //AISM. 2019. Vol. in press. P. 1-30.     
  5. Girardin V., Konev V.V., Pergamenshchikov S. M. Kullback-Leibler Approach to CUSUM Quickest Detection Rule for Markovian Time Series //Sequential Analysis. 2018. Vol. 37, № 3. P. 322-341.
  6. Yury G. Dmitriev, Peter F. Tarassenko, Yuri K. Ustinov. Determinacy Analysis of Weights as Mathematical Basis of the Future Sociology //ACSR. 2017. Vol. 72. P. 238-243.
  7. Yury G. Dmitriev, Gennady M. Koshkin, Vadim Yu. Lukov. Combined Identification and Prediction Algorithms //ACSR. 2017. Vol. 72. P. 244-247.
  8.  Livshits K., Kitaeva A., Ulyanova E. Steady State Probabilistic Characteristics of the On/Off Production Rate Control Production-Inventory System with MMPP Demand Arrivals //CCIS. 2018. Vol. 912. P. 248-262.           
  9. Kitaeva A.V., Livshits K.I., Ulyanova E.S. Estimating the Demand Parameters for Single Period Problem, Markov-modulated Poisson Demand, Large Lot Size, and Unobserved Lost Sales //IFAC-PapersOnline. 2018. Vol. 51, № 11. P. 882-887.      
  10. Kitaeva A.V., Zhukovskaya A.O., Zmeev O.A. Compound Poisson demand with price-dependent intensity for fast moving items: price ptimization and parameters estimation //International Journal of Production Research. 2017. Vol. 55, № 14. P. 4153-4163. URL: http://dx.doi.org/10.1080/00207543.2016.1257168 (date of access: 21.11.2016).
  11. Kitaeva A.V., Stepanova N.V., Zukovskaya A. O. Pricing and Lot-Sizing for Continuously Decaying Items with Stochastic Demand //IFAC-PapersOnline. 2017. Т. 50, № 1. С. 10160-10165.  
  12. Kitaeva A., Livshits K., Ulyanova E. The Multi-product Newsboy Problem with Price-Depended Demand and Fast Moving Items //CCIS. 2017. Vol. 800. P. 297-311.