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A Stochastic Ordering Property for Leaky Bucket Regulated Flows in Packet Networks

  • Fabrice M. Guillemin (a1), Ravi R. Mazumdar (a2), Catherine P. Rosenberg (a2) and Yu Ying (a3)

Abstract

We show in this paper that if a stationary traffic source is regulated by a leaky bucket with leak rate ρ and bucket size σ, then the amount of information generated in successive time intervals is dominated, in the increasing convex ordering sense, by that of a Poisson arrival process with rate ρ/σ, with each arrival bringing an amount of information equal to σ. By exploiting this property, we then show that the mean value in the stationary regime of the content of a buffer drained at constant rate and fed with the superposition of regulated flows is less than the mean value of the same buffer fed with an adequate Poisson process, whose characteristics depend upon the regulated input flows.

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Copyright

Corresponding author

Postal address: France Telecom, 2 Avenue Pierre Marzin, 22300 Lannion, France. Email address: fabrice.guillemin@orange-ftgroup.com
∗∗ Postal address: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
∗∗∗ Email address: mazum@ece.uwaterloo.ca
∗∗∗∗ Email address: cath@ece.uwaterloo.ca
∗∗∗∗∗ Postal address: School of ECE, Purdue University, West Lafayette, IN 47907, USA. Email address: yingy@purdue.edu

References

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[16] Ying, Y., Guillemin, F., Mazumdar, R. and Rosenberg, C. (2005). Buffer overflow asymptotics for multiplexed regulated traffic. To appear in Performance Evaluation.

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