Skip to main content
Log in

Analysis of a buffer queueing problem in discrete time

  • Contributed Papers
  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

We consider a queueing system with bulk arrivals entering a finite waiting room. Service is provided by a single server according to the limited service discipline with server vacation times. We determine the distributions of the time-dependent and stationary queue length in terms of generating functions by a symbolic operator method.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. Bruneel, Analysis of an infinite buffer system with random server interruptions, Comp. & Ops. Res. 11 (1984) 373–386.

    Google Scholar 

  2. J.F. Chang and R.F. Chang, The application of the residue theorem to the study of a finite queue with batch Poisson arrivals and synchronous servers, SIAM J. Appl. Math. 44 (1984) 646–656.

    Google Scholar 

  3. J.W. Cohen,On Regenerative Processes in Queueing Theory (Springer Berlin-Heidelberg-New York, 1976).

    Google Scholar 

  4. G.W. Forbes, Truncation and manipulation of multivariate power series, J. Comp. and Appl. Math. 15 (1986) 27–36.

    Google Scholar 

  5. G.H. Hsu and K. Bosch, Finite dams with double level of release, Z.O.R. 27 (1983) 83–106.

    Google Scholar 

  6. J.J. Hunter,Mathematical Techniques of Applied Probability, Vol. 2: Discrete Models: Techniques and Applications (Academic Press, New York-San Francisco-London, 1983).

    Google Scholar 

  7. M. Kramer, Wartesysteme beschränkter Kapazität mit Sperrphasen und relativen Prioritäten, in: Messung, Modellierung und Bewertung von Rechensystemen, eds. P.J. Kühn and K.M. Schulz, Informatik-Fachberichte Nr. 61, 150–164 (Springer Berlin-Heidelberg-New York, 1983).

    Google Scholar 

  8. M. Kramer, Computational analysis of a queueing system with vacation times and non-exhaustive service, Stochastic Models 4 (1988) 151–159.

    Google Scholar 

  9. N.U. Prabhu,Queues and Inventories (J. Wiley, New York-London-Sydney, 1965).

    Google Scholar 

  10. H. Takagi,Analysis of Polling Systems (MIT Press, Cambridge Mass., 1986).

    Google Scholar 

  11. M. Zafirovic-Vukotic and I.G. Niemegeers, Analytical models of the slotted ring protocols in HSLANs, in:High Speed Local Area Networks, eds. O. Spaniol and A. Danthine (North-Holland, Amsterdam-New York-Oxford-Tokyo, 1987) 115–134.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kramer, M. Analysis of a buffer queueing problem in discrete time. Queueing Syst 5, 369–379 (1989). https://doi.org/10.1007/BF01225325

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01225325

Keywords

Navigation