Skip to main content
SpringerLink
Log in
Book cover

International Conference on Analytical and Computational Methods in Probability Theory

ACMPT 2017: Analytical and Computational Methods in Probability Theory pp 265–278Cite as

Sensitivity Analysis of Reliability and Performability Measures for a Multi-server Queueing System with Constant Retrial Rate

  • Conference paper
  • First Online:

  • 611 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10684))

Abstract

The paper deals with the sensitivity analysis of reliability and performance measures for a multi-server queueing system where customers at the head of the queue retries to occupy a server in exponentially distributed time. The servers can differ in service and reliability characteristics. We have proved the insensitivity of the mean number of customers in the system to the type of allocation policy for equal service rates and confirmed a weak sensitivity in a general case of unequal service rates. A further sensitivity analysis is conducted to investigate the effect of changes in system parameters on a reliability function, a distribution of the number of failures of a server and a maximum queue length during a life time.

This is a preview of subscription content, 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

Learn about institutional subscriptions

References

  1. Artalejo, J.R., Gomez-Corral, A., Neuts, M.F.: Analysis of multiserver queues with constant retrial rate. Eur. J. Oper. Res. 135(3), 569–581 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Artalejo, J.R., Falin, G.: Standard and retrial queueing systems: a comparative analysis. Revista Matematica Complutense XV(1), 101–129 (2002)

    MathSciNet  MATH  Google Scholar 

  3. Efrosinin, D., Rykov, V.: Sensitivity analysis of reliability characteristics to the shape of the life and repair time distributions. In: Dudin, A., Nazarov, A., Yakupov, R., Gortsev, A. (eds.) ITMM 2014. CCIS, vol. 487, pp. 101–112. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13671-4_13

    Google Scholar 

  4. Efrosinin, D., Sztrik, J.: Performance analysis of a two-server heterogeneous retrial queue with threshold policy. Qual. Technol. Quant. Manag. 3, 211–236 (2011)

    Article  Google Scholar 

  5. Özkan, E., Kharoufeh, J.P.: Optimal control of a two-server queueing system with failures. Probab. Eng. Inf. Sci. 28(14), 489–527 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Puterman, M.L.: Markov Decision Processes: Dyscrete Stochastic Dynamic Programming. Wiley, Hoboken (2005)

    MATH  Google Scholar 

  7. Roszik, J., Sztrik, J.: Performance analysis of finite-source retrial queues with non-reliable heterogenous servers. J. Math. Sci. 146(4), 6033–6038 (2007)

    Article  MathSciNet  Google Scholar 

  8. Rykov, V., Kozyrev, D., Zaripova, E.: Modeling and simulation of reliability function of a homogeneous hot double redundant repairable system. In: Paprika, Z.Z., et al. (eds.) ECMS 2017, Proceedings European Council for Modeling and Simulation (2017)

    Google Scholar 

Download references

Acknowledgements

The publication was prepared with the support of the “RUDN University Program 5-100”, RFBR according to the research project No. 16-37-60072 mol.a.dk.

Author information

Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya str. 6, Moscow, 117198, Russia

    Dmitry Efrosinin

  2. Institute for Control Sciences, RAS, Profsoyuznaya str. 65, Moscow, 117997, Russia

    Dmitry Efrosinin

Authors
  1. Dmitry Efrosinin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitry Efrosinin .

Editor information

Editors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Vladimir V. Rykov

  2. City University of Hong Kong, Hong Kong, Hong Kong

    Nozer D. Singpurwalla

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Andrey M. Zubkov

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Efrosinin, D. (2017). Sensitivity Analysis of Reliability and Performability Measures for a Multi-server Queueing System with Constant Retrial Rate. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-71504-9_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71503-2

  • Online ISBN: 978-3-319-71504-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation