On-Off Fluid Models in Heavy Traffic Environment

@article{Debicki1999OnOffFM,
  title={On-Off Fluid Models in Heavy Traffic Environment},
  author={Krzysztof Debicki and Zbigniew Palmowski},
  journal={Queueing Syst.},
  year={1999},
  volume={33},
  pages={327-338}
}
We consider fluid models with infinite buffer size. Let {ZN (t)} be the net input rate to the buffer, where {ZN (t)} is a superposition of N homogeneous alternating on–off flows. Under heavy traffic environment {ZN (t)} converges in distribution to a centred Gaussian process with covariance function of a single flow. The aim of this paper is to prove the convergence of the stationary buffer content process {X∗ N (t)} in the N th model to the buffer content process {X∗(t)} in the limiting… CONTINUE READING
Highly Cited
This paper has 19 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 24 references

A note on LDP for supremum of Gaussian processes over infinite horizon

  • K. Dȩbicki
  • Statist. Probab. Lett. 44
  • 1999
Highly Influential
5 Excerpts

The superposition of alternating on–off flows and a fluid model

  • Z. Palmowski, T. Rolski
  • Ann. Appl. Probab. 8(2)
  • 1998
Highly Influential
8 Excerpts

Multiple time scale and subexponential asymptotic behaviour of a network multiplexer

  • P. R. Jelenković, A. A Lazar
  • in: Stochastic Networks: Stability and Rare…
  • 1996
Highly Influential
2 Excerpts

Fluid model driven by an Ornstein–Uhlenbeck process

  • V. Kulkarni, T. Rolski
  • Probab. Engrg. Inform. Sci. 8
  • 1994
Highly Influential
5 Excerpts

Central limit theorems in D[0

  • M. J. Hahn
  • 1], Wahrscheinlichkeitstheorie Verw. Gebiete 44
  • 1978
Highly Influential
2 Excerpts

Weak convergence of probability measures and random functions in the function space D[0,∞)

  • T. Lindvall
  • J. Appl. Probab
  • 1973
Highly Influential
2 Excerpts

Similar Papers

Loading similar papers…