A GAUSSIAN FLUID MODEL

A fluid model with infinite buffer is considered. The total net rate is a stationary Gaussian process with mean -c and covariance function R(t). Let Psi(x) be the probability that in steady state conditions the buffer content exceeds x. Under the condition integral(0)(infinity) t(2) \ R(t) \ dt < infinity we show that Psi admits a logarithmic linear upper bound, i.e. Psi(x) less than or equal to C exp[-gamma x]) o(exp[-gamma x]) and find gamma and C. Special cases are worked out when Ii is as in a Gauss-Markov or AR-Gaussian process.