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Queueing systems for multiple FBM-based traffic models

Published online by Cambridge University Press:  17 February 2009

Mihaela T. Matache  and
Valentin Matache
Mihaela T. Matache
Affiliation:
Department of Mathematics, The University of Nebraska at Omaha, Omaha, NE 68182, USA: e-mail: dmatache@mail.unomaha.edu and vmatache@mail.unomaha.edu.
Valentin Matache
Affiliation:
Department of Mathematics, The University of Nebraska at Omaha, Omaha, NE 68182, USA: e-mail: dmatache@mail.unomaha.edu and vmatache@mail.unomaha.edu.
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Abstract

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A multiple fractional Brownian motion (FBM)-based traffic model is considered. Various lower bounds for the overflow probability of the associated queueing system are obtained. Based on a probabilistic bound for the busy period of an ATM queueing system associated with a multiple FBM-based input traffic, a minimal dynamic buffer allocation function (DBAF) is obtained and a DBAF-allocation algorithm is designed. The purpose is to create an upper bound for the queueing system associated with the traffic. This upper bound, called a DBAF, is a function of time, dynamically bouncing with the traffic. An envelope process associated with the multiple FBM-based traffic model is introduced and used to estimate the queue size of the queueing system associated with that traffic model.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 3 , January 2005 , pp. 361 - 377
Copyright
Copyright © Australian Mathematical Society 2005

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