Abstract
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 Ψ(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 Ψ admits a logarithmic linear upper bound, i.e. Ψ(x)≤Cexp[−γx]+o(exp[−γx]) and find γ and C. Special cases are worked out whenR is as in a Gauss-Markov or AR-Gaussian process.
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Debicki, K., Rolski, T. A Gaussian fluid model. Queueing Syst 20, 433–452 (1995). https://doi.org/10.1007/BF01245328
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DOI: https://doi.org/10.1007/BF01245328