Numerical Inversion of Transforms Occurring in Queueing and Other Stochastic Processes

We consider the numerical inversion of three classes of generating functions (GFs): classes of probability generating functions (PGFs) that are given in rational and non-rational forms, and a class of GFs that are not PGFs. Particular emphasis is on those PGFs that are not explicitly given but contain a number of unknowns. We show that the desired sequence can be obtained to any given accuracy, so long as enough numerical precision is used.