Skip to main content
SpringerLink
Log in

Regeneration and renovation in queues

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

Regenerative events for different queueing models are considered. The aim of this paper is to construct these events for continuous-time processes if they are given for the corresponding discrete-time model. The construction uses so-called renovative events revealing the property of the state at timen of the discrete-time model to be independent (in an algebraic sense) of the states referring to epochs not later thann −L (whereL is some constant) given that there are some restrictions on the “governing sequence”. Different types of multi-server and multi-phase queues are considered.

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. S. Asmussen,Applied Probability and Queues (Wiley, 1987).

  2. S. Asmussen and S. Foss, Renovation, regeneration and coupling in multi-server queues in continuous time, Preprint No. 1990-2, Dept. of Math., Chalmers Univ. of Technology, The University of Göteborg (1990), to appear in Ann. Appl. Prob.

  3. A. Borovkov,Asymptotic Methods in Queueing Theory (Nauka, Moscow, 1980) (in Russian). (English translation: Wiley, 1984).

    Google Scholar 

  4. A. Borovkov, Limit theorems for queueing networks I, Theory Prob. Appl. 31 (1986) 474–490.

    Article  Google Scholar 

  5. S. Foss, On conditions of ergodicity for multi-server queues, Sibirsk. Math. Zhurnal 24 (1983) 168–175 (in Russian).

    Google Scholar 

  6. S. Foss, The method of renovation events and its applications in queueing theory,Semi-Markov Models. Theory and Application, Proc. 1-st Int. Symp. on Semi-Markov Processes, Brussel (1984) (Plenum, 1986) pp. 337–350.

  7. S. Foss, On some properties of open queueing networks, Probl. Inf. Transmission 25 (1989) 90–97.

    Google Scholar 

  8. V. Kalashnikov,Qualitative Analysis of Complex Systems Behaviour by Test Functions Method (Nauka, Moscow, 1978) (in Russian).

    Google Scholar 

  9. V. Kalashnikov, Stability estimates for renovative processes, Eng. Cybern. 17 (1980) 85–89.

    Google Scholar 

  10. V. Kalashnikov, Regenerative queueing processes and their qualitative and quantitative analysis, Queueing Systems 6 (1990) 113–136.

    Google Scholar 

  11. V. Kalashnikov and S. Rachev,Mathematical Methods for Construction of Queueing Models (Wadsworth and Brooks/Cole, 1990).

  12. E. Nummelin,General Irreducible Markov Chains and Non-Negative Operators (Cambridge Univ. Press, 1984).

  13. H. Thorisson, The coupling of regenerative processes, Adv. Appl. Prob. 15 (1983) 531–561.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, USSR

    S. G. Foss

  2. Institute for Systems Studies, 9, Prospect 60 let Oktjabrja, 117312, Moscow, USSR

    V. V. Kalashnikov

Authors
  1. S. G. Foss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Kalashnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Foss, S.G., Kalashnikov, V.V. Regeneration and renovation in queues. Queueing Syst 8, 211–223 (1991). https://doi.org/10.1007/BF02412251

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02412251

Keywords

Search

Navigation