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- Joseph Abate, Ward Whitt
- Queueing Syst.
- 1992

This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf’s) and probability mass functions (pmf’s) by numerically inverting characteristic functions,… (More)

- Joseph Abate, Ward Whitt
- INFORMS Journal on Computing
- 1995

The purpose of this document is to summarize main points of the paper, “Numerical Inversion of Laplace Transforms of Probability Distributions”, and provide R code for the Euler method that is… (More)

- Joseph Abate, Ward Whitt
- Queueing Syst.
- 1997

We consider the classical M/G/1 queue with two priority classes and the nonpreemptive and preemptive-resume disciplines. We show that the low-priority steady-state waiting-time can be expressed as a… (More)

- Joseph Abate, Ward Whitt
- INFORMS Journal on Computing
- 2006

where the weights ωk and nodes αk are complex numbers, which depend on n, but do not depend on the transform f̂ or the time argument t. Many different algorithms can be put into this framework,… (More)

1.1 INTRODUCTION Numerical transform inversion has an odd place in computational probability. Historically, transforms were exploited extensively for solving queueing and related probability models,… (More)

In this paper we establish asymptotics for the basic steady-state distributions in a large class of single-server queues. We consider the waiting time, the workload (virtual waiting time) and the… (More)

- Joseph Abate, Gagan L. Choudhury, Ward Whitt
- INFORMS Journal on Computing
- 1996

The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 Tricomi-Widder theorem, which shows (under suitable regularity conditions) that the… (More)

- Joseph Abate, Gagan L. Choudhury, Ward Whitt
- Queueing Syst.
- 1994

We consider the standard GI/G/1 queue with unlimited waiting room and the first-in first-out service discipline. We investigate the steady-state waiting-time tail probabilities P(W > x) when the… (More)

- Joseph Abate, Ward Whitt
- Queueing Syst.
- 1987

This paper presents some new perspectives on the time-dependent behavior of the M / M / 1 queue. The factorial moments of the queue length as functions of time when the queue starts empty have… (More)

- Harvey Dubner, Joseph Abate
- J. ACM
- 1968

In this paper the problem of readily determining the inverse Laplace transform numerically by a method which meets the efficiency requirements of automatic digital computation is discussed. Because… (More)