Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T20:04:31.786Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on the strong limiting behaviour of busy periods in GI/G/1 queues under heavy traffic

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Josef Steinebach  and
Hanqin Zhang
Josef Steinebach*
Affiliation:
Philipps University, Marburg
Hanqin Zhang*
Affiliation:
Philipps University, Marburg
*
Postal address for both authors: Department of Mathematics, Philipps University, Hans-Meerwein-Strasse, DW-3550, Marburg, Germany.
Postal address for both authors: Department of Mathematics, Philipps University, Hans-Meerwein-Strasse, DW-3550, Marburg, Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this note, the strong limiting behaviour of busy periods in GI/G/1 queues is studied under the condition that the traffic intensity equals unity.

Keywords

BUSY CYCLESTOPPING TIME

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60F15: Strong theorems 60K05: Renewal theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 483 - 488
Copyright
Copyright © Applied Probability Trust 1993 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

∗

On leave from the Institute of Applied Mathematics, Academia Sinica, Beijing, China. Research supported by DAAD-K.C. Wong Fellowship.

References

Alex, M. and Steinebach, J. (1989) Invariance principles in queueing theory. J. Appl. Prob. 27, 845–857.CrossRefGoogle Scholar
Chow, Y. S. and Teicher, H. (1988) Probability Theory, 2nd edn. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Gut, A. (1988) Stopped Random Walks. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Iglehart, D. L. (1973) Weak convergence in queueing theory. Adv. Appl. Prob. 5, 570–594.CrossRefGoogle Scholar
Kesten, H. (1971) Sums of random variables with infinite expectation. Amer. Math. Monthly 78, 305–308.CrossRefGoogle Scholar
Spitzer, F. (1960) A Tauberian theorem and its probability interpretation. Trans. Amer. Math. Soc. 94, 150–169.CrossRefGoogle Scholar