THE TAIL BEHAVIOR OF THE STATIONARY DISTRIBUTION OF A FLUID QUEUE WITH A GAUSSIAN-TYPE INPUT RATE PROCESS

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This paper deals with a fluid queue with a Gaussian-type input rate process. The Gaussian-type processes are ones defined as R_t = m + f^t_<-∞> h(t - s)dw_s, where m is a positive constant, w_t is a standard Wiener process and h(t) is an integrable function such that h(t)^2 and H(t) = f^∞_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) = f^∞_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].
社団法人日本オペレーションズ・リサーチ学会の論文