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.

This work is financed by national funds through FCT - Fundação para a Ciência e Tecnologia, I.P., under the project FCT UIDB/04466/2020. Furthermore, the author thanks the Iscte-Instituto Universitário de Lisboa and ISTAR-IUL, for their support.

algorithm,busy period,Laplace transform,M|G|∞,queues network

• Matemáticas - Ciências Naturais
• Ciências da Computação e da Informação - Ciências Naturais