Skip to main content
SpringerLink
Log in

Joint distributions in Poissonian tandem queues

  • Articles
  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

A pair of single server queues arranged in series is considered. The input flow is Poisson and service times are mutually independent and exponentially distributed in each station. The joint distributions of the stationary waiting times and queue lengths at the arrival epoch are treated.

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. P.J. Burke, The dependence of delays in tandem queues, Ann. Math. Stat. 35 (1964) 874–875.

    Google Scholar 

  2. J.M. Harrison, The heavy traffic approximation for single server queues in series, J. Appl. Probab. 10 (1973) 613–629.

    Google Scholar 

  3. J.M. Harrison, The diffusion approximation for tandem queues in heavy traffic, Adv. Appl. Probab. 10 (1978) 886–905.

    Google Scholar 

  4. J.R. Jackson, Networks of waiting lines, Oper. Res. 5 (1957) 518–521.

    Google Scholar 

  5. Yu.F. Jackushev, On two-stage service of recurrent input, Proc. Acad. Sci. USSR, Engin. Cybern. 3 (1973) 115–119.

    Google Scholar 

  6. S.F. Jashkoff, Invariance properties of the stochastic models of time-sharing systems, Autom. Control Comput. 6 (1980) 56–62.

    Google Scholar 

  7. F.I. Karpelevitch and A.Ya. Kreinin, Two-phase queueing systemGI/G/1/∞→G/1/∞ under heavy traffic conditions, Theory Probab. Appl. 26 (1981) 302–320.

    Google Scholar 

  8. F.P. Kelly, Reversibility and Stochastic Networks (Wiley, 1979).

  9. R.M. Loynes, On the waiting time distribution for queues in series, J. Roy. Stat. Soc. Ser. B 27 (1965) 491–496.

    Google Scholar 

  10. I. Mitrani, A critical note on a result by Lemoine, Manag. Sci. 25 10 (1979) 1026–1027.

    Google Scholar 

  11. E. Reich, Waiting times when queues are in tandem, Ann. Math. Statist. 28 (1957) 768–783.

    Google Scholar 

  12. E. Reich, Note on queues in tandem, Ann. Math. Stat. 34 (1963) 338–341.

    Google Scholar 

  13. W. Szczotka and F.P. Kelly, Asymptotic stationarity of queues in series and the heavy traffic approximation, Ann. Probab. 18 (1990) 1232–1248.

    Google Scholar 

  14. Xi-Ren Cao, The dependence of sojourn times on service times in tandem queues, J. Appl. Probab. 21 (1984) 661–667.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Institute for Railway Transport Engineering, Moscow Institute for Controlling Computers and LVS Corporation, Kropotkinskaya 17/8/9-2, Moscow, Russia

    F. I. Karpelevitch & A. Ya. Kreinin

Authors
  1. F. I. Karpelevitch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Ya. Kreinin
    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

Karpelevitch, F.I., Kreinin, A.Y. Joint distributions in Poissonian tandem queues. Queueing Syst 12, 273–286 (1992). https://doi.org/10.1007/BF01158803

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158803

Keywords

Search

Navigation