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Stationary Analysis of a Fluid Queue with Input Rate Varying as an Ornstein-Uhlenbeck Process

Alain Simonian
SIAM Journal on Applied Mathematics
Vol. 51, No. 3 (Jun., 1991), pp. 828-842
Stable URL: http://www.jstor.org/stable/2102051
Page Count: 15
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Stationary Analysis of a Fluid Queue with Input Rate Varying as an Ornstein-Uhlenbeck Process
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Abstract

The stationary probability distribution of the content of a fluid queue with constant output rate and input rate varying as an Ornstein-Uhlenbeck process is studied. Markov properties provide the set of equations for the derivation of this distribution; the consideration of its Fourier transform leads to the study of a functional equation of integral type in the complex plane. This analysis is shown to relate to that of the connected Fokker-Planck equation. Results are discussed and compared to that of a similar fluid queueing model. This study was motivated by teletraffic problems encountered in the multiplexing of video communications with variable activity rate.

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