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Smoothing effect of the superposition of homogeneous sources in tandem networks

Part of: Stochastic processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Arie Hordijk ,
Zhen Liu  and
Don Towsley
Arie Hordijk*
Affiliation:
University of Leiden
Zhen Liu*
Affiliation:
INRIA
Don Towsley*
Affiliation:
University of Massachusetts
*
∗Postal address: Mathematical Institute, University of Leiden, The Netherlands
∗∗Postal address: INRIA, 2004 Route des Lucioles, B.P. 93, 06902 Sophia Antipolis, France. Email address: liu@sophia.inria.fr
∗∗∗Postal address: Department of Computer Science, University of Massachusetts, Amherst, MA 01003, USA
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Abstract

We analyze the smoothing effect of superposing homogeneous sources in a network. We consider a tandem queueing network representing the nodes that customers generated by these sources pass through. The servers in the tandem queues have different time varying service rates. In between the tandem queues there are propagation delays. We show that for arbitrary arrival and service processes which are mutually independent, the sum of unfinished works in the tandem queues is monotone in the number of homogeneous sources in the increasing convex order sense, provided the total intensity of the foreground traffic is constant. The results hold for both fluid and discrete traffic models.

Keywords

Homogeneous sourcestraffic superpositionstochastic comparisonmultiplexing gain

MSC classification

Primary: 90B15: Network models, stochastic 90B18: Communication networks
Secondary: 60G20: Generalized stochastic processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 900 - 913
Copyright
Copyright © Applied Probability Trust 2000 

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Footnotes

The work of this author was supported in part by NSF under awards ANI-980933 and CDA-9502639

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