Skip to main content
SpringerLink
Log in

Detailed Analysis of the Response Time and Waiting Time in the M/M/m FCFS Preemptive-Resume Priority Queue

  • Conference paper
Queueing Theory and Network Applications (QTNA 2015)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 383))

Included in the following conference series:

Abstract

We present a detail theoretical analysis of the response time and waiting time in the M/M/m FCFS preemptive-resume priority queueing system in the steady state by scrutinizing and extending the previous studies by Brosh (1969), Segal (1970), Buzen and Bondi (1983), Tatashev (1984), and Zeltyn et al. (2009). In particular, we analyze the durations of intermittent waiting times and service times during the response time of a tagged customer of each priority class that is preempted by the arrivals of higher-priority class customers. Numerical examples are shown in order to demonstrate the computation of theoretical formulas.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brosh, I.: Preemptive priority assignment in multichannel systems. Operations Research 17(3), 526–535 (1969)

    Article  Google Scholar 

  2. Buzen, J.P., Bondi, A.B.: The response times of priority classes under preemptive resume in M/M/\( m \) queues. Operations Research 31(3), 456–465 (1983)

    Article  Google Scholar 

  3. Fujiki, M.: Fundamental theory and application on communication traffic. 5 queuein theory (part 2). Transactions of the Institute of Electronics and Communication Engineers of Japan 55(9), 1194–1200 (1972). (in Japanese)

    Google Scholar 

  4. Segal, M.: A multiserver system with preemptive priorities. Operations Research 18(2), 316–323 (1970)

    Article  Google Scholar 

  5. Tatashev, A.G.: Calculation of the distribution of the waiting time in a multiple-channel queueing system with fixed priorities. Engineering Cybernetics 22(1), 59–62 (1984). (Originally published in Tekhnicheskaya Kibernetika, No.6, pp. 163–166 (1983)

    MathSciNet  MATH  Google Scholar 

  6. Zeltyn, S., Feldman, Z., Wasserkrug, S.: Waiting and sojourn times in a multi-server queue with mixed priorities. Queueing Systems 61(4), 305–328 (2009)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Professor Emeritus, University of Tsukuba, Tsukuba Science City, Ibaraki, 305-8573, Japan

    Hideaki Takagi

Authors
  1. Hideaki Takagi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hideaki Takagi .

Editor information

Editors and Affiliations

  1. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary

    Tien van Do

  2. Department of Systems Science, Kyoto University Graduate School of Informatics, Kyoto, Japan

    Yutaka Takahashi

  3. Faculty of Science and Engineering, Department of Information Science and Systems Engineering, Konan University, Kobe, Japan

    Wuyi Yue

  4. Faculty of Information Technology, VNU University of Engineering and Technology, Hanoi, Vietnam

    Viet-Ha Nguyen

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Takagi, H. (2016). Detailed Analysis of the Response Time and Waiting Time in the M/M/m FCFS Preemptive-Resume Priority Queue. In: van Do, T., Takahashi, Y., Yue, W., Nguyen, VH. (eds) Queueing Theory and Network Applications. QTNA 2015. Advances in Intelligent Systems and Computing, vol 383. Springer, Cham. https://doi.org/10.1007/978-3-319-22267-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22267-7_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22266-0

  • Online ISBN: 978-3-319-22267-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation