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

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Fabrice M. Guillemin ,
Ravi R. Mazumdar ,
Catherine P. Rosenberg  and
Yu Ying
Fabrice M. Guillemin*
Affiliation:
France Telecom
Ravi R. Mazumdar*
Affiliation:
University of Waterloo
Catherine P. Rosenberg*
Affiliation:
University of Waterloo
Yu Ying*
Affiliation:
Purdue University
*
∗ Postal address: France Telecom, 2 Avenue Pierre Marzin, 22300 Lannion, France. Email address: [email protected]
∗∗ Postal address: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
∗∗ Postal address: Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
∗∗∗∗∗ Postal address: School of ECE, Purdue University, West Lafayette, IN 47907, USA. Email address: [email protected]
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Abstract

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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.

Keywords

Stochastic orderingfluid queueregulated flows

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 90B15: Network models, stochastic 90B18: Communication networks 90B20: Traffic problems
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 332 - 348
Copyright
Copyright © Applied Probability Trust 2007 

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