Solving probability transform functional equations for numerical inversion

Authors:
Joseph Abate;Ward Whitt
Affiliations:
900 Hammond Road, Ridgewood, NJ 07450-2908, USA;AT&T Bell Laboratories, Murray Hill, NJ 07974-0636, USA
Venue:
Operations Research Letters
Year:
1992

Citing 4
Cited 2

The Fourier-series method for inverting transforms of probability distributions

Queueing Systems: Theory and Applications - Numerical computations in queues
Busy Period Analysis of a Time-Sharing System: transform inversion

Journal of the ACM (JACM)
Algorithm 368: Numerical inversion of Laplace transforms [D5]

Communications of the ACM
Numerical inversion of probability generating functions

Operations Research Letters

Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion

Operations Research Letters
On the numerical inversion of busy-period related transforms

Operations Research Letters

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Abstract

Many methods for numerically inverting transforms require values of the transform at complex arguments. However, in some applications, the transforms are only characterized implicitly via functional equations. This is illustrated by the busy-period distribution in the M/G/1 queue. In this paper we provide conditions for iterative methods to converge for complex arguments. Moreover, we show that stochastic monotonicity properties can provide useful bounds.