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Queueing Systems - Eindhoven University of Technology

2.3 Laplace-Stieltjes transform The Laplace-Stieltjes transform Xf(s) of a nonnegative random variable Xwith distribution function F(), is de ned as Xf(s) = E(e sX) = Z 1 x=0 e sxdF(x); s 0: When the random variable Xhas a density f(), then the transform simpli es to Xf(s) = Z 1 x=0 e sxf(x)dx; s 0: Note that jXf(s)j 1 for all s 0. Further

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  System, Queueing, Transform, Laplace, Queueing systems

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