Skip to main content
SpringerLink
Log in

Generating function analysis of some joint distributions for Poisson loss systems

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

We present a new approach to derive joint distributions for stationary Poisson loss systems. In particular, for M/M/m/0 and M/M/1/n we find the Laplace transforms (with respect to time t) of the probability that at time t there are i customers in the system and during [0,t], j customers are refused admission; for M/M/m/0 we further determine the LT of the probability that the system was full for less than s time units during [0,t] and serves i customers at time t. Explicit formulas for the corresponding moments are also given.

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. J.W. Cohen, The Single-Server Queue (North-Holland, Amsterdam, 1982).

  2. A. Erdélyi, ed., Higher Transcendental Functions, Vol. II (McGraw-Hill, New York, 1953).

    Google Scholar 

  3. B.W. Gnedenko and D. König, Handbuch der Bedienungstheorie II (Akademie-Verlag, Berlin, 1984).

    Google Scholar 

  4. F.N. Gouweleeuw, Calculating the loss probability in a BMAP/G/1/N+1 queue, Stochastic Models 12 (1996) 473–492.

    Google Scholar 

  5. F.N. Gouweleeuw, A general approach to computing loss probabilities in finite-buffer queues, in: Ten Years LNMB, eds. W.K. Klein Haneveld et al., CWI Tracts 122 (1997) pp. 131–134.

  6. T. Homma and S. Ninonija, Some results for queueing systems M/M/s(N +s), Yokohama Math. J. 14 (1966) 1–16.

    Google Scholar 

  7. I.N. Kovalenko and J.B. Atkinson, On the calculation of steady-state loss probabilities in the GI/G/2/0 queue, J. Math. Stochastic Anal. 7 (1994) 397–410.

    Google Scholar 

  8. A. Kuczura, Loss systems with mixed renewal and Poisson inputs, Oper. Res. 21 (1973) 787–795.

    Google Scholar 

  9. J. Riordan, Stochastic Service Systems (Wiley, New York, 1962).

    Google Scholar 

  10. L. Takács, Introduction to the Theory of Queues (Oxford Univ. Press, New York, 1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    W. Stadje

  2. Department of Mathematics, Indian Institute of Technology, Madras, India

    P.R. Parthasarathy

Authors
  1. W. Stadje
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P.R. Parthasarathy
    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

Stadje, W., Parthasarathy, P. Generating function analysis of some joint distributions for Poisson loss systems. Queueing Systems 34, 183–197 (2000). https://doi.org/10.1023/A:1019157019655

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019157019655

Search

Navigation