Skip to main content
SpringerLink
Log in

On Loss Process in a Queueing System Operating Under Single Vacation Policy

  • Conference paper
  • First Online:
Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017 (ISAT 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 656))

Abstract

A finite-buffer queueing model with Poisson arrivals and generally distributed processing times is analyzed. Every time when the service station becomes idle a single vacation period is being initialized, during which the processing is suspended. A system of integral equations for the probability distribution of the length of the first loss series is built, using the idea of embedded Markov chain and the total probability law. The solution of the is obtained in a compact form by using the linear algebraic approach. The corresponding result for next series of losses is hence derived. Numerical utility of analytical formulae is presented in a computational example.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. de Boer, P.T., Nicola, V.F., van Ommeren, J.C.W.: The remaining service time upon reaching a high level in M/G/1 queues. Queueing Syst. 39, 55–78 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chae, K.C., Kim, K., Kim, N.K.: Remarks on the remaining service time upon reaching a target level in the M/G/1 queue. Oper. Res. Lett. 35, 308–310 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chydziński, A.: On the remaining service time upon reaching a target level in M/G/1 queues. Queueing Syst. 47, 71–80 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fakinos, D.: The expected remaining service time in a single server queue. Oper. Res. 30, 1014–1018 (1982)

    Article  MATH  Google Scholar 

  5. Kempa, W.M.: On the distribution of the time to buffer overflow in a queueing system with a general-type input stream. In: 35th International Conference on Telecommunication and Signal Processing (TSP 2012), pp. 207–211, Piscataway, Prague, Czech Republic, 3–4 July 2012

    Google Scholar 

  6. Kempa, W.M.: On transient queue-size distribution in the batch-arrivals system with a single vacation policy. Kybernetika 50, 126–141 (2014)

    MathSciNet  MATH  Google Scholar 

  7. Kempa, W.M.: On queueing delay in WSN with energy saving mechanism based on queued wake up. In: Mustra, M., et al. (eds.) Proceedings of 21st International Conference on Systems, Signals and Image Processing (IWSSIP 2014), pp. 187–190, Zagreb, Dubrovnik, Croatia, 12–15 May 2014

    Google Scholar 

  8. Kempa, W.M.: Time-dependent analysis of transmission process in a wireless sensor network with energy saving mechanism based on threshold waking up. In: IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2015), pp. 26–30, Piscataway, Stockholm, Sweden, 28 June–1 July 2015

    Google Scholar 

  9. Kempa, W.M.: Transient workload distribution in the M/G/1 finite-buffer queue with single and multiple vacations. Ann. Oper. Res. 239, 381–400 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kempa, W.M., Paprocka, I.: Time to buffer overflow in a finite-capacity queueing model with setup and closedown times. In: Świątek, J., Wilimowska, Z., Borzemski, L., Grzech, A. (eds.) Proceedings of 37th International Conference on Information Systems Architecture and Technology (ISAT 2016), Part 3. Advances in Intelligent Systems and Computing, vol. 523, pp. 215–224. Springer, Cham (2017)

    Google Scholar 

  11. Korolyuk, V.S.: Boundary-value Problems for Compound Poisson Processes. Naukova Dumka, Kiev (1975)

    MATH  Google Scholar 

  12. Woźniak, M., Kempa, W.M., Gabryel, M., Nowicki, R.: A finite-buffer queue with a single vacation policy: an analytical study with evolutionary positioning. Int. J. Appl. Math. Comput. Sci. 24, 887–900 (2014)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Applied Mathematics, Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 2A, 44-100, Gliwice, Poland

    Wojciech M. Kempa

Authors
  1. Wojciech M. Kempa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wojciech M. Kempa .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Computer Science and Management, Wrocław University of Science and Technology, Wrocław, Poland

    Jerzy Świątek

  2. Department of Computer Science, Faculty of Computer Science and Management, Wrocław University of Science and Technology, Wrocław, Poland

    Leszek Borzemski

  3. Department of Management Systems, Faculty of Computer Science and Management, Wrocław University of Science and Technology, Wrocław, Poland

    Zofia Wilimowska

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Kempa, W.M. (2018). On Loss Process in a Queueing System Operating Under Single Vacation Policy. In: Świątek, J., Borzemski, L., Wilimowska, Z. (eds) Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017. ISAT 2017. Advances in Intelligent Systems and Computing, vol 656. Springer, Cham. https://doi.org/10.1007/978-3-319-67229-8_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67229-8_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67228-1

  • Online ISBN: 978-3-319-67229-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation