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Weak convergence of high-speed network traffic models

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Sidney Resnick  and
Eric van den Berg
Sidney Resnick*
Affiliation:
Cornell University
Eric van den Berg*
Affiliation:
Telecordia Technologies
*
∗Postal address: School of Operations Research and Industrial Engineering, Cornell University, 206 Rhodes Hall, Ithaca, NY 14853-3801, USA. Email address: [email protected]
∗∗Postal address: Telecordia Technologies, 445 South Street, Room 16338B, Movistown, NJ 07960, USA. Email address: [email protected]
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Abstract

We consider a network traffic model consisting of an infinite number of sources linked to a server. Sources initiate transmissions to the server at Poisson time points. The duration of each transmission has a heavy-tailed distribution. We show that suitable scalings of the traffic process converge to a totally skewed stable Lévy motion in Skorohod space, equipped with the Skorohod M1 topology. This allows us to prove a heavy-traffic theorem for a single-server fluid model.

Keywords

Fractional Brownian motionPoisson processLévy stable motionhigh speed networkM1 Topology

MSC classification

Primary: 90B15: Network models, stochastic 90B18: Communication networks
Secondary: 90B22: Queues and service 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 575 - 597
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

This research was partly supported by NSF Grant DMS-97-04982 at Cornell University. S. Resnick was also partially supported by NSA grant MDA904-98-1-0041 at Cornell. Portions of this work were completed at the University of North Carolina, Chapel Hill, and the hospitality of the Department of Statistics is gratefully acknowledged.

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