Skip to main content
SpringerLink
Log in

Algorithms for the Analysis of Queueing System M/G/1/\(\infty \) with Cut-Off of the Line

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

The classical queueing system M/G/1 is considered for a case when the service begins, if the number of waited claims reaches the fixed level k. Various algorithms are considered for the calculation of such indices as the mean and the distribution of the waiting time, the queue length and so on.

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

Access this article

Log in via an institution

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. Pollaczek, F., Über eine Aufgabe der Wahrscheinlichkeitstheorie. I, Math. Z., 1930, vol. 32, pp. 64–100.  https://doi.org/10.1007/BF01194620

    Article  MathSciNet  MATH  Google Scholar 

  2. Khintchine, A.Y., Mathematical theory of a stationary queue, Math. Sb., 1932, vol. 39, no. 4, pp. 73–84.

    Google Scholar 

  3. Abate, J., Choudhury, G.L., and Whitt, W., Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion, Oper. Res. Lett., 1995, vol. 18, no. 3, pp. 113–119.  https://doi.org/10.1016/0167-6377(95)00049-6

    Article  MathSciNet  MATH  Google Scholar 

  4. Abouee-Mehrizi, H. and Baron, O., State-dependent M/G/1 queueing systems, Queueing Syst., 2016, vol. 82, pp. 121–148.  https://doi.org/10.1007/s11134-015-9461-y

    Article  MathSciNet  MATH  Google Scholar 

  5. Asmussen, S., Ladder heights and the Markov-modulated M/G/1 queue, Stochastic Processes Their Appl., 1991, vol. 37, no. 2, pp. 313–326.  https://doi.org/10.1016/0304-4149(91)90050-M

    Article  MathSciNet  MATH  Google Scholar 

  6. Bekker, R. and Boxma, O.J., An M/G/1 queue with adaptable service speed, Stochastic Mod., 2007, vol. 23, no. 3, pp. 373–396.  https://doi.org/10.1080/15326340701470945

    Article  MathSciNet  MATH  Google Scholar 

  7. Regterschot, G.J.K. and de Smit, J.H.A., The Queue M|G|1 with Markov modulated arrivals and services, Math. Oper. Res., 1986, vol. 11, no. 3, p. 385–535.  https://doi.org/10.1287/moor.11.3.465

    Article  MathSciNet  MATH  Google Scholar 

  8. Rolski, T., Serfozo, R., and Stoyan, D., Service-time ages, residuals, and lengths in an M/GI/∞ service system, Queueing Syst., 2015, vol. 79, pp. 173–181.  https://doi.org/10.1007/s11134-014-9420-z

    Article  MathSciNet  MATH  Google Scholar 

  9. Servi, L.D. and Finn, S.B., M/M/1 queues with working vacations (M/M/1/WV), Perform. Eval., 2002, vol. 50, no. 1, pp. 41–52.  https://doi.org/10.1016/S0166-5316(02)00057-3

    Article  Google Scholar 

  10. Tain, N. and Zhang, G., Vacation Queueing Models: Theory and Applications, Vol. 1: Vacation and Priority Systems. Part 1, Amsterdam: Elsevier Science Publ., 1990.

    Google Scholar 

  11. Doshi, B.T., Queueing systems with vacations – A survey, Queueing Syst., 1986, vol. 1, pp. 29–66.  https://doi.org/10.1007/BF01149327

    Article  MathSciNet  MATH  Google Scholar 

  12. Doshi, B.T., A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times, J. Appl. Probab., 1985, vol. 22, no. 2, pp. 419–428.  https://doi.org/10.2307/3213784

    Article  MathSciNet  MATH  Google Scholar 

  13. Levy, H. and Kleinrock, L.O., A queue with starter and a queue with vacations: Delay analysis by decomposition, Oper. Res., 1986, vol. 34, no. 3, pp. 345–493.  https://doi.org/10.1287/opre.34.3.426

    Article  MathSciNet  MATH  Google Scholar 

  14. Lucantoni, D.M., Meier-Hellstern, K.S., and Neuts, M.F., A single-server queue with server vacations and a class of non-renewal arrival processes, Adv. Appl. Probab., 1990, vol. 22, no. 3, pp. 676–705.  https://doi.org/10.2307/1427464

    Article  MathSciNet  MATH  Google Scholar 

  15. Gnedenko, B.V. and Kovalenko, I.N., Vvedenie v teoriyu massovogo obsluzhivaniya (Introduction to Queueing Theory), Moscow: Nauka, 1987.

  16. Cox, D.R. and Smith, W.L., Queues, London: Methuen & Co, 1961.

    Google Scholar 

  17. Smith, W.L. and Stoneley, R., Regenerative stochastic processes, Proc. R. Soc. London, Ser. A, 1955, vol. 232, no. 1188, pp. 6–31.  https://doi.org/10.1098/rspa.1955.0198

    Article  MathSciNet  MATH  Google Scholar 

  18. Pacheco, A., Tang, L.Ch., and Prabhu, N.U., Markov-Modulated Processes and Semiregenerative Phenomena, New Jersey: World Scientific, 2008.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Transport and Telecommunication Institute, 226019, Riga, Latvia

    A. M. Andronov

  2. Saint-Petersburg State University of Civil Aviation, 196210, St. Petersburg, Russia

    I. M. Dalinger

Authors
  1. A. M. Andronov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. M. Dalinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. M. Andronov or I. M. Dalinger.

Ethics declarations

The authors declare that they have no conflicts of interest.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Andronov, A.M., Dalinger, I.M. Algorithms for the Analysis of Queueing System M/G/1/\(\infty \) with Cut-Off of the Line. Aut. Control Comp. Sci. 56, 95–108 (2022). https://doi.org/10.3103/S014641162202002X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S014641162202002X

Keywords:

Search

Navigation