In this report we study the suprema distribution of a class of Gaussian processes having stationary increments and negative drift using key results from ~Txtrerne Value Theory. We focus on deriving an asymptotic upper bound to the tail of the suprema distribution of such processes. Our bound is valid for both discrete- and continuous-time processes. VVe discuss the importance of the bound, its applicability to queueing problems, and show numerical examples to illustrate its performance.
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