Skip to main content
SpringerLink
Log in
Book cover

Stochastic Orders in Reliability and Risk pp 351–361Cite as

On a Slow Server Problem

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 208))

Abstract

The slow server problem is generalized for the case of additional cost structure. With the help of special partial ordering of the system state space it is shown that the optimal policy for the problem has a monotone property consisting in the following: an additional server should be switched on only in the case if the queue length exceeds some level depending on the system state, and in this case the server with minimal service cost should be used.

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   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Bibliography

  1. Efrosinin, D.: Controlled queueing systems with heterogeneous servers: Dynamic optimization and monotonicity properties. Saarbrücken: VDM Verlag (2008)

    Google Scholar 

  2. Efrosinin, D. and Breuer, L.: Threshold policies for controlled retrial queues with heterogeneous servers. Annals of Operations Research, 141, 139–162 (2006)

    Article  MathSciNet  Google Scholar 

  3. Hajek, B.: Optimal control of two interacting service stations. IEEE Transactions on Automatic Control, 29, 491–499 (1984)

    Article  MATH  Google Scholar 

  4. Kitaev, M. Y. and Rykov, V. V.: Controlled queueing systems. CRC Press, New York (1995)

    MATH  Google Scholar 

  5. Koole, G.: A simple proof of the optimality of a threshold policy in two-server queueing system. Systems & Control Letters, 26, 301–303 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Krishnamoorthy, B.: On Poisson queue with two heterogeneous servers. Operational Research, 11, 321–330 (1963)

    Article  Google Scholar 

  7. Langrock, P. and Rykov V. V.: Methoden und Modelle zur Steurung von Bedienungssystemen. Handbuch der Bedienungs theorie. Berlin, Akademie-Verlag, B. 2, 422–486 (1984)

    Google Scholar 

  8. Lin, W. and Kumar, P. R.: Optimal control of a queueing system with two heterogeneous servers. IEEE Transactions on Automatic Control, 29, 696–703 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pedro, T.: One size does not fit all: a case for heterogeneous multiprocessor systems. IADIS International Conference Applied Computing, 15–22 (2005)

    Google Scholar 

  10. Rykov, V. V.: On monotonicity conditions of optimal control policies for controllable Queueing Systems. Automation and Remote Control, 9, 92–106 (1999)

    MathSciNet  Google Scholar 

  11. Rykov, V. V.: Monotone Control of Queueing System with heterogeneous servers. Queueing Systems, 37, 391–403 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Rykov, V. V. and Efrosinin, D. V.: Numerical study of optimal control of queueing system with heterogeneous servers. Automation and Remote Control, 64(2), 302–309 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rykov, V. V. and Efrosinin, D. V.: On slow Server Problem. Automation and Remote Control, 70(12), 2013–2023 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sennott, L. I.: Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York (1999)

    MATH  Google Scholar 

  15. Vericourt, F. and Zhou, Y. P.: On the incomplete results for the heterogeneous server problem. Queueing Systems, 52, 189–191 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Vishnevsky, V. M. and Semenova, O. V.: Polling systems: theory and applications in bandwidth wireless networks (in Russian). M.: Tekhnosppere (2007)

    Google Scholar 

  17. Weber, R.: On a conjecture about assigning jobs to processors of different speeds. IEEE Transactions on Automatic Control, 38, no. 1, 166–170 (1993)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Computational Modeling, Gubkin Russian State University of Oil and Gas, Moscow, 119991, Leninsky prosp. 65, Russia

    Vladimir Rykov

Authors
  1. Vladimir Rykov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Rykov .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Washington State University, Lighty 370, Pullman, 99164, Washington, USA

    Haijun Li

  2. Xiamen University, Xiamen, 361000, China, People's Republic

    Xiaohu Li

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Rykov, V. (2013). On a Slow Server Problem. In: Li, H., Li, X. (eds) Stochastic Orders in Reliability and Risk. Lecture Notes in Statistics(), vol 208. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6892-9_18

Download citation

Publish with us

Policies and ethics

Search

Navigation