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Analysis of the fluid weighted fair queueing system

Published online by Cambridge University Press:  14 July 2016

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.

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2003 

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References

[1] Clark, D., Shenker, S., and Zhang, L. (1992). Supporting real time applications in an integrated services packet network: architecture and mechanism. In Proc. SIGCOMM Annual Tech. Conf.’92, Association for Computing Machinery, New York, pp. 1426.Google Scholar
[2] Cohen, J. W., and Boxma, O. J. (1984). Boundary Value Problems in Queueing System Analysis (North-Holland Math. Studies 79). North-Holland, Amsterdam.Google Scholar
[3] Dautray, R., and Lions, J. L. (1985). Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques. Masson, Paris.Google Scholar
[4] Fayolle, G., and Iasnogorodski, R. (1979). Two coupled processors: the reduction to a Riemann–Hilbert problem. Z. Wahrscheinlichkeitsth. 47, 325351,Google Scholar
[5] Fayolle, G., Iasnogorodski, R., and Malyshev, V. (1999). Random Walks in the Quarter-Plane (Appl. Math. 40). Springer, Berlin.Google Scholar
[6] Fayolle, G., King, P. J. B., and Mitrani, I. (1982). The solution of certain two-dimensional Markov models. Adv. Appl. Prob. 14, 295308.CrossRefGoogle Scholar
[7] Kleinrock, L. (1975). Queueing Systems, Vol. I, Theory. John Wiley, New York.Google Scholar
[8] Rudin, W. (1965). Real and Complex Analysis. McGraw-Hill, New York.Google Scholar
[9] Schiffmann, G. (1984). Analyse Complexe. École Polytechnique, Palaiseau.Google Scholar