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Sharp Bounds on Laplace-Stieltjes Transforms, with Applications to Various Queueing Problems

Several partial characterizations of positive random variables (e.g., certain moments) are considered. For each characterization, sharp upper and lower bounds on the Laplace-Stieltjes transform of the corresponding distribution function are derived. These bounds are then shown to be applicable to several problems in queueing and traffic theory. The results can prove useful in producing conservative estimates of a system's performance, in judging the information content of a partial characterization and in providing insight into approximations.