Laplace Transform in the Context Some M|G|∞ Queue Associated Probability Distributions - Ferreira, M. A. M. (EasyChair Preprint no. 13822, 2025)
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 chapter it is considered a situation not so simple, as it is the case of the length of the MG∞ queue busy period distribution. Attention will also be given the respective tail Laplace transform. Then, in the context of a queues network, which nodes behave as MG∞ queues, the Laplace transform will be used to construct an algorithm to determine the Laplace transform of the distribution of the global service time length of a customer during their stay on the network.