The tail behavior of the stationary distribution of a fluid queue with a Gaussian-type input rate process

The tail behavior of the stationary distribution of a fluid queue with a Gaussian-type input rate process

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Article ID: iaor1998461
Country: Japan
Volume: 40
Issue: 1
Start Page Number: 75
End Page Number: 89
Publication Date: Mar 1997
Journal: Journal of the Operations Research Society of Japan
Authors: ,
Keywords: statistics: regression
Abstract:

This paper deals with a fluid queue with a Gaussian-type input rate process. The Gaussian-type processes are ones defined as Rt = m + ∫t−∞ h(t−s)dws, where m is a positive constant, wt is a standard Wiener process and h(t) is an integrable function such that h(t)2 and H(t) = ∫t h(s)ds are also integrable. The class of Gaussian-type processes is wide enough to contain most of continuous time stochastic processes proposed so far for coded video traffic. For the model, in this paper, the exponential decay property of the tail of the buffer content distribution is studied, and an upper bound and a lower one are given for the tail probability P(Q > x) of the buffer content distribution in the steady state. These bounds show that the tail probability decays exponentially with rate − (C−m)/(H(0)2/2), where H(0) = ∫0 h(t)dt and C is the output rate of the fluid queue. This result guarantees, in a sense, the plausibility of the approximation formula P(Q > x) ≈ B exp {−((C−m)/(H(0)2/2))x} proposed in the previous paper [Performance Evaluation, 1995].

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