Skip to main content
SpringerLink
Log in

Vacation and Polling Models with Retrials

  • Conference paper
Computer Performance Engineering (EPEW 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8721))

Included in the following conference series:

Abstract

We study a vacation-type queueing model, and a single-server multi-queue polling model, with the special feature of retrials. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) arriving at the station during this glue period will be served during the visit of the server. Customers arriving in any other period leave immediately and will retry after an exponentially distributed time. Our main focus is on queue length analysis, both at embedded time points (beginnings of glue periods, visit periods and switch- or vacation periods) and at arbitrary time points.

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 39.99
Price excludes VAT (USA)
  • Available as 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antunes, N., Fricker, C., Roberts, J.: Stability of multi-server polling system with server limits. Queueing Systems 68, 229–235 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. Antunes, N., Fricker, C., Robert, P., Roberts, J.: Traffic capacity of large WDM Passive Optical Networks. In: Proceedings 22nd International Teletraffic Congress, ITC 22, Amsterdam (September 2010)

    Google Scholar 

  3. Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems: A Computational Approach. Springer, Berlin (2008)

    Book  Google Scholar 

  4. Athreya, K.B., Ney, P.E.: Branching Processes. Springer, Berlin (1972)

    Book  MATH  Google Scholar 

  5. Boon, M.A.A., van der Mei, R.D., Winands, E.M.M.: Applications of polling systems. SORMS 16, 67–82 (2011)

    Google Scholar 

  6. Boxma, O.J., Cohen, J.W.: The M/G/1 queue with permanent customers. IEEE J. Sel. Areas in Commun. 9, 179–184 (1991)

    Article  Google Scholar 

  7. Falin, G.I., Templeton, J.G.C.: Retrial Queues. Chapman and Hall, London (1997)

    Book  MATH  Google Scholar 

  8. Koonen, A.M.J.: Personal communication (2014)

    Google Scholar 

  9. Langaris, C.: A polling model with retrial of customers. Journal of the Operations Research Society of Japan 40, 489–507 (1997)

    MATH  MathSciNet  Google Scholar 

  10. Langaris, C.: Gated polling models with customers in orbit. Mathematical and Computer Modelling 30, 171–187 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Langaris, C.: Markovian polling system with mixed service disciplines and retrial customers. Top 7, 305–322 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Levy, H., Sidi, M.: Polling models: Applications, modeling and optimization. IEEE Trans. Commun. 38, 1750–1760 (1990)

    Article  Google Scholar 

  13. Maier, M.: Optical Switching Networks. Cambridge University Press, Cambridge (2008)

    Google Scholar 

  14. Olsen, T.L., van der Mei, R.D.: Periodic polling systems in heavy traffic: Distribution of the delay. Journal of Applied Probability 40, 305–326 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Quine, M.P.: The multitype Galton-Watson process with immigration. Journal of Applied Probability 7, 411–422 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  16. Resing, J.A.C.: Polling systems and multitype branching processes. Queueing Systems 13, 409–426 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Rogiest, W.: Stochastic Modeling of Optical Buffers. Ph.D. Thesis, Ghent University, Ghent, Belgium (2008)

    Google Scholar 

  18. Takagi, H.: Application of polling models to computer networks. Comput. Netw. ISDN Syst. 22, 193–211 (1991)

    Article  Google Scholar 

  19. Takagi, H.: Queueing Analysis: A Foundation of Performance Evaluation. Vacation and Priority Systems, vol. 1. Elsevier Science Publishers, Amsterdam (1991)

    MATH  Google Scholar 

  20. Takagi, H.: Queueing analysis of polling models: progress in 1990-1994. In: Dshalalow, J.H. (ed.) Frontiers in Queueing: Models, Methods and Problems, pp. 119–146. CRC Press, Boca Raton (1997)

    Google Scholar 

  21. Takagi, H.: Analysis and application of polling models. In: Reiser, M., Haring, G., Lindemann, C. (eds.) Dagstuhl Seminar 1997. LNCS, vol. 1769, pp. 424–442. Springer, Heidelberg (2000)

    Google Scholar 

  22. Vishnevskii, V.M., Semenova, O.V.: Mathematical methods to study the polling systems. Autom. Remote Control 67, 173–220 (2006)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Onno Boxma & Jacques Resing

Authors
  1. Onno Boxma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacques Resing
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dip. di Informatica, Università di Torino, 10149, Turin, Italy

    András Horváth

  2. Freie Universität Berlin, Takustr. 9, 14195, Berlin, Germany

    Katinka Wolter

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Boxma, O., Resing, J. (2014). Vacation and Polling Models with Retrials. In: Horváth, A., Wolter, K. (eds) Computer Performance Engineering. EPEW 2014. Lecture Notes in Computer Science, vol 8721. Springer, Cham. https://doi.org/10.1007/978-3-319-10885-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10885-8_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10884-1

  • Online ISBN: 978-3-319-10885-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation