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Analysis of the fluid weighted fair queueing system

Part of: Special processes Computer system organization

Published online by Cambridge University Press:  14 July 2016

Fabrice Guillemin ,
Ravi Mazumdar ,
Alain Dupuis  and
Jacqueline Boyer
Fabrice Guillemin*
Affiliation:
France Télécom
Ravi Mazumdar*
Affiliation:
Purdue University
Alain Dupuis*
Affiliation:
France Télécom
Jacqueline Boyer*
Affiliation:
France Télécom
*
∗ Postal address: France Télécom R&D, 2, Avenue Pierre Marzin, 22300 Lannion, France.
∗∗∗ Postal address: School of Electrical and Computer Engineering, MSEE Building, Room 342, Purdue University, West-Lafayette, IN 47907-1285, USA.
∗ Postal address: France Télécom R&D, 2, Avenue Pierre Marzin, 22300 Lannion, France.
∗ Postal address: France Télécom R&D, 2, Avenue Pierre Marzin, 22300 Lannion, France.
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Abstract

We analyse in this paper the fluid weighted fair queueing system with two classes of customers, who arrive according to Poisson processes and require arbitrarily distributed service times. In a first step, we express the Laplace transform of the joint distribution of the workloads in the two virtual queues of the system by means of unknown Laplace transforms. Such an unknown Laplace transform is related to the distribution of the workload in one queue provided that the other queue is empty. We explicitly compute the unknown Laplace transforms by means of a Wiener—Hopf technique. The determination of the unknown Laplace transforms can be used to compute some performance measures characterizing the system (e.g. the mean waiting time for each class) which we compute in the exponential service case.

Keywords

Weighted fair queueing disciplinecoupled servercomplex analysisWiener—Hopf technique

MSC classification

Primary: 68M20: Performance evaluation; queueing; scheduling
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 180 - 199
Copyright
Copyright © Applied Probability Trust 2003 

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References

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