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Anisotropic scaling of the random grain model with application to network traffic

Part of: Stochastic processes Special processes

Published online by Cambridge University Press:  24 October 2016

Vytautė Pilipauskaitė  and
Donatas Surgailis
Vytautė Pilipauskaitė*
Affiliation:
Université de Nantes and Vilnius University
Donatas Surgailis*
Affiliation:
Vilnius University
*
* Postal address: Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania.
* Postal address: Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania.
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Abstract

We obtain a complete description of anisotropic scaling limits of the random grain model on the plane with heavy-tailed grain area distribution. The scaling limits have either independent or completely dependent increments along one or both coordinate axes and include stable, Gaussian, and ‘intermediate’ infinitely divisible random fields. The asymptotic form of the covariance function of the random grain model is obtained. Application to superimposed network traffic is included.

Keywords

Random grain modelanisotropic scalinglong-range dependenceLévy sheetfractional Brownian sheetworkload process

MSC classification

Primary: 60G60: Random fields
Secondary: 60G22: Fractional processes, including fractional Brownian motion 60G51: Processes with independent increments; L'evy processes 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 3 , September 2016 , pp. 857 - 879
Copyright
Copyright © Applied Probability Trust 2016 

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