The Laplace transform in the context of some of the queue related probability distributions

The Laplace transform is a widely used tool in the study of probability distributions, often allowing for a simpler determination of the p.d.f.'s and d.f.'s, and having the possibility to work as a “moments generating function”. In this paper it is considered a situation not so simple, as it is the case of the queue busy period length distribution. Attention will also be given the respective tail Laplace transform. Then, in the context of an open queues network, which nodes behave as queues, the Laplace transform will be used to construct an algorithm to determine the Laplace transform of the global service time length of a customer during their stay on the network distribution.