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 functionR(t). Let (x) be the probability that in steady state conditions the buffer content exceedsx. Under the condition ₀ t ² ¦R(t)¦dt< we show that admits a logarithmic linear upper bound, i.e. (x)Cexp–x]+o(exp–x]) and find and C. Special cases are worked out whenR is as in a Gauss-Markov or AR-Gaussian process.