Skip to main content
SpringerLink
Log in

Optimization of Uniform Non-Markov Queueing Networks Using Resources and Transition Probabilities Redistribution

  • Conference paper
  • First Online:
Information Technologies and Mathematical Modelling - Queueing Theory and Applications (ITMM 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 638))

Abstract

An efficient analytic-imitational method for optimization of uniform non-Markov queueing networks is proposed. The optimization is performed through resources and transition probabilities redistribution by the minimal mean time of the request staying in the network. The convergence rate and precision of the method are evaluated experimentally. The method allows the optimization of the networks with hundreds of single- and multi-channel nodes with precision comparable to the one of the numerical methods for deterministic problems solution. Examples of the method’s application in transport modeling are given. Practical application recommendations are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Vishnevskiy, V.M.: Theoretical Bases of Designing Computer Networks, 512 p. Technosphere, Moscow (2003)

    Google Scholar 

  2. Kleinrock, L.: Queueing Systems, Computer Applications, vol. 2, 576 p. Wiley Interscience, New York (1976)

    Google Scholar 

  3. Vishnevskiy, V.M., Porotskiy, C.M.: Simulation of departmental e-mail systems. Autom. Teleautomatics 12, 48–57 (1996). (in Russian)

    Google Scholar 

  4. Zhozhikashvili, V.A., Vishnevskiy, V.M.: Queueing Networks. Theory and Applications to Computer Networks, 192 p. Radio i Svyaz, Moscow (1988). (in Russian)

    Google Scholar 

  5. Ferrari, D.: Performance Evaluation of Computer Systems, 554 p. Prentice-Hall (1978)

    Google Scholar 

  6. Gerasimov, A.I.: Optimization of closed queuing networks with several classes of messages. Probl. Transmitting Inform. 30(1), 85–96 (1994). (in Russian)

    MathSciNet  MATH  Google Scholar 

  7. Ryizhikov, Y.: Simulation Modeling. Theory and Technology, 384 p. KORONA print, St. Petersburg. Alteks-A, Moscow (2004). (in Russian)

    Google Scholar 

  8. Kleinrock, L.: Queueing Systems, Theory, vol. 1, 417 p. Wiley (1975)

    Google Scholar 

  9. Bitran, G.R.: Open Queueing Networks: Optimization and Performance Evaluation Models for Discrete Manufacturing Systems / Gabriel R. Bitran, Reinaldo Morabito, 47 p. URL:http://dspace.mit.edu/bitstream/handle/1721.1/2537/SWP-3743-31904719.pdf. (Accessed date, 01 Nov 2012)

  10. Kleijnen, J.P.C.: Statistical Techniques in Simulation, Part 1. Marcel Dekker, New York (1974)

    MATH  Google Scholar 

  11. Johnson, M.E., Jackson, J.: Infinitesimal perturbation analysis: a tool for simulation. J. Oper. Res. Soc. 40(3), 134–160 (1989)

    Article  Google Scholar 

  12. Rubinstein, R.Y.: Sensitivity analysis of computer simulation models via the efficient score. Operat. Res. 37, 72–81 (1989)

    Article  Google Scholar 

  13. Suri, R., Zazanis, M.: Perturbation analysis gives strongly consistent sensitivity estimates for the M—G—1 queue. MGMT Sci. 34, 39–64 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  14. Iglehart, D.L., Shedler, G.S. (eds.): Regenerative Simulation of Response Times in Networks of Queues. LNCIS, vol. 26. Springer, Heidelberg (1980)

    MATH  Google Scholar 

  15. Tsitsiashvili, G.: Sh. Parametric and structural optimization of the queuing network throughput. Autom. Remote Control 68(7), 1177–1185 (2007). doi:10.1134/S0005117907070065. PACS number: 89.75.Fb 2007

    Article  MathSciNet  MATH  Google Scholar 

  16. Zadorozhnyi, V.N.: Analytical-Simulation Research of Queuing Systems and Networks, 280 p. Omsk State Technical University Publishing House, Omsk (2010). (in Russian)

    Google Scholar 

  17. Zadorozhnyi, V.N.: Optimizing uniform non-markov queueing networks. Autom. Remote Control 71(6), 1158–1169 (2010). doi:10.1134/S0005117910060172. ISSN 0005–1179

    Article  MATH  Google Scholar 

  18. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms, 854 p. A John Wiley and Sons, Inc. (2006)

    Google Scholar 

  19. Nazarov, A., Moiseev, A.N.: Investigation of the queueing network GI(GI\(|\infty )^K\) by means of the first jump equation and asimptotic analysis. In: Vishnevsky, V., Kozyrev, D., Larionov, A. (eds.) DCCN 2013. CCIS, vol. 279, pp. 229–240. Springer, Heidelberg (2014)

    Google Scholar 

  20. Moiseev, A.A., Nazarov, A.N.: Infinitely Linear Systems and Queuing Networks, 240 p. NTL Publishing House, Tomsk (2015). (in Russian)

    Google Scholar 

  21. Zadorozhnyi, V.N.: Optimization highly redundant Markov chains with queues. Omskiy Nauchnyiy Vest. 3(123), 21–25 (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Omsk State Technical University, Omsk, Russia

    Vladimir N. Zadorozhnyi

Authors
  1. Vladimir N. Zadorozhnyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir N. Zadorozhnyi .

Editor information

Editors and Affiliations

  1. Belarusian State University , Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University , Tomsk, Russia

    Alexander Gortsev

  3. Tomsk State University , Tomsk, Russia

    Anatoly Nazarov

  4. Kemerovo State University , Anzhero-Sudzhensk, Russia

    Rafael Yakupov

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Zadorozhnyi, V.N. (2016). Optimization of Uniform Non-Markov Queueing Networks Using Resources and Transition Probabilities Redistribution. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2016. Communications in Computer and Information Science, vol 638. Springer, Cham. https://doi.org/10.1007/978-3-319-44615-8_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-44615-8_32

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44614-1

  • Online ISBN: 978-3-319-44615-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation