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Fluid Model Driven by an Ornstein-Uhlenbeck Process

Published online by Cambridge University Press:  27 July 2009

Vidyadhar Kulkarni  and
Tomasz Rolski
Vidyadhar Kulkarni
Affiliation:
Department of Operations Research, CB# 3180, Smith Building, University of North Carolina, Chapel Hill, North Carolina 27599–3180
Tomasz Rolski
Affiliation:
Mathematical Institute, The University of Wroclaw, pl. Grunwaldzki 2/4 50 384 Wroclaw, Poland
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Abstract

In this paper we consider a fluid model of a single buffer in a random external environment modeled by an Ornstein-Uhlenbeck process. Such a model appears as the limiting case of the multiplexing model of Anick, Mitra, and Sondhi [2] in a heavy traffic environment. We use the change of measure technique to derive an exponential upper bound on the tail probabilities of the steady-state buffer content. We also establish an asymptotic upper and lower exponential bounds on the tail probabilities.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 3 , July 1994 , pp. 403 - 417
Copyright
Copyright © Cambridge University Press 1994

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