Skip to main content

M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis

  • Conference paper
  • First Online:
Quantitative Evaluation of Systems (QEST 2020)

Abstract

We propose an analytical method for an M/M/1 vacation queue with workload dependent service rates. We obtain the distribution of the workload in the system, and consider a power-saving and performance trade-off problem. Numerical experiments reveal that square root service rate function has lower cost than that of linear and quadratic service functions under certain scenarios.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Kankaya, H.E., Akar, N.: Solving multi-regime feedback fluid queues. Stochast. Models 24(3), 425–450 (2008)

    Article  MathSciNet  Google Scholar 

  2. Marin, A., Mitrani, I., Elahi, M., Williamson, C.: Control and optimization of the SRPT service policy by frequency scaling. In: McIver, A., Horvath, A. (eds.) QEST 2018. LNCS, vol. 11024, pp. 257–272. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99154-2_16

    Chapter  Google Scholar 

  3. Phung-Duc, T.: Exact solutions for M/M/c/Setup queues. Telecommun. Syst. 64(2), 309–324 (2016). https://doi.org/10.1007/s11235-016-0177-z

    Article  MathSciNet  Google Scholar 

  4. Sakuma, Y., Boxma, O., Phung-Duc, T.: A single server queue with workload-dependent service speed and vacations. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds.) QTNA 2019. LNCS, vol. 11688, pp. 112–127. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-27181-7_8

    Chapter  MATH  Google Scholar 

  5. Yajima, M., Phung-Duc, T.: Batch arrival single-server queue with variable service speed and setup time. Queueing Syst. 86(3–4), 241–260 (2017)

    Article  MathSciNet  Google Scholar 

  6. Yazici, M.A., Akar, N.: The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity. Perform. Eval. 70(12), 1047–1058 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mehmet Akif Yazici .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Yazici, M.A., Phung-Duc, T. (2020). M/M/1 Vacation Queue with Multiple Thresholds: A Fluid Analysis. In: Gribaudo, M., Jansen, D.N., Remke, A. (eds) Quantitative Evaluation of Systems. QEST 2020. Lecture Notes in Computer Science(), vol 12289. Springer, Cham. https://doi.org/10.1007/978-3-030-59854-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-59854-9_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59853-2

  • Online ISBN: 978-3-030-59854-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics