Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

The M/G/1+G queue revisited

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous model in which any customer enters the system and leaves at the end of his patience time or at the end of his virtual sojourn time, whichever occurs first.

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

Access this article

Log in via an institution

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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Baccelli, F., Hébuterne, G.: On queues with impatient customers. In: Kylstra, F.J. (ed.) Performance’81, pp. 159–179. North-Holland, Amsterdam (1981)

    Google Scholar 

  2. Baccelli, F., Boyer, P., Hébuterne, G.: Single-server queues with impatient customers. Adv. Appl. Probab. 16, 887–905 (1984)

    Article  Google Scholar 

  3. Bae, J., Kim, S., Lee, E.Y.: The virtual waiting time of the M/G/1 queue with impatient customers. Queueing Syst. 38, 485–494 (2001)

    Article  Google Scholar 

  4. Barrer, D.Y.: Queuing with impatient customers and ordered service. Oper. Res. 5, 650–656 (1957)

    Article  Google Scholar 

  5. Boxma, O.J., Perry, D.: On the cycle maximum of mountains, dams and queues. Comm. Stat., Theory Methods 38, 2706–2720 (2009). Special issue in honor of Shelley Zacks

    Article  Google Scholar 

  6. Boxma, O.J., Perry, D., Stadje, W., Zacks, S.: The M/G/1 queue with quasi-restricted accessibility. Stoch. Models 25, 151–196 (2009)

    Article  Google Scholar 

  7. Boxma, O.J., Perry, D., Stadje, W., Zacks, S.: The busy period of an M/G/1 queue with customer impatience. J. Appl. Probab. 47, 130–145 (2010)

    Article  Google Scholar 

  8. Finch, P.D.: Deterministic customer impatience in the queueing system GI/M/1. Biometrika 47, 45–52 (1960)

    Google Scholar 

  9. Gavish, B., Schweitzer, P.J.: The Markovian queue with bounded waiting time. Manag. Sci. 23, 1349–1357 (1977)

    Article  Google Scholar 

  10. Perry, D., Asmussen, S.: Rejection rules in the M/G/1 queue. Queueing Syst. 19, 105–130 (1995)

    Article  Google Scholar 

  11. Perry, D., Stadje, W., Zacks, S.: Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility. Oper. Res. Lett. 27, 163–174 (2000)

    Article  Google Scholar 

  12. Stanford, R.E.: Reneging phenomena in single channel queues. Math. Oper. Res. 4, 162–178 (1979)

    Article  Google Scholar 

  13. Stanford, R.E.: On queues with impatience. Adv. Appl. Probab. 22, 768–769 (1990)

    Article  Google Scholar 

  14. Subba Rao, S.: Queuing models with balking and reneging. Ann. Inst. Math. Jpn. 19, 55–71 (1967)

    Google Scholar 

  15. Subba Rao, S.: Queuing with balking and reneging in M/G/1 systems. Metrika 6, 173–188 (1967/1968)

    Article  Google Scholar 

  16. Takács, L.: Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York (1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, HG 9.14, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Onno Boxma

  2. Department of Statistics, University of Haifa, Haifa, 31909, Israel

    David Perry

  3. Department of Mathematics and Computer Science, University of Osnabrück, 49069, Osnabrück, Germany

    Wolfgang Stadje

Authors
  1. Onno Boxma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Perry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wolfgang Stadje
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Perry.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boxma, O., Perry, D. & Stadje, W. The M/G/1+G queue revisited. Queueing Syst 67, 207–220 (2011). https://doi.org/10.1007/s11134-010-9205-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11134-010-9205-y

Keywords

Mathematics Subject Classification (2000)

Search

Navigation