On the numerical inversion of busy-period related transforms
Most algorithms for the numerical inversion of integral transforms require the values of the involved transforms at complex arguments. This poses a problem for inverting transforms implicitly defined as solutions of some functional equations. A number of examples of such transforms stem from queueing theory, e.g. the number of customers in a busy period and the busy period distribution. The author shows that the original contour integral with an implicitly defined integrand needed to invert the transform can be replaced by alternative contour integrals with only known transforms as part of the integrand. This method is applied to the two above mentioned queueing problems.
scientific article; zbMATH DE number 1790722