Publications with Joseph Abate
Collaboration with Joe Abate began in the mid 80's while we both were at Bell Labs.
Joe had earned a Ph.D. in theoretical physics from Courant Institute (New York University)
in 1967,
after which he did engineering and performance analysis. Joe was at AT&T Bell
Laboratories from 1971 to 1990. When we met, Joe was at the Whippany facility,
leading a group
in the development of capacity models and performance analysis tools
for the Loop Maintenance Operations Support (LMOS) system  a large online computer
system which supports loop repair operations for telephone
companies (i.e., handling "611" calls). Joe subsequently led a group at Whippany
developing an experimental signal processing system, concerned with
processing active sonar signals to support longrange surveillance,
to meet "the silent threat". That experience (vicarious for me)
enhanced my reading
of The Hunt for the Red October.
In addition to having a strong practical engineering focus, Joe has
a passion for serious research
and scholarship. Joe is interested in the "grundlagen", wanting to
understand what is fundamental and wanting to put important ideas
in proper historical perspective.
Thus, throughout his career, Joe has
pursued research interests in his spare time
(when he is not cooking or gardening), focusing on
Laplace transforms, numerical transform inversion,
classical applied mathematics (especially asymptotics
associated with Laplace transforms)
and queueing models.
So, back in the 80's I was fortunate to have a phone call from Joe.
I had done a few papers focusing
on ways to obtain simple approximations to describe queueing performance,
and Joe wanted to discuss some of his ideas.
That initial interaction
led to an active research collaboration.
The two main topics of our joint research became:
(1) exact and approximate methods to describe the transient behavior
of queues and
(2) numerical transform inversion.
Laplace transforms and
numerical transform inversion
are used throughout our work, from the very beginning.
When we started, I knew little (was totally ignorant)
about these interesting and useful tools
(and much of classical applied mathematics, more generally).
I have been fortunate to have Joe as a teacher, helping me to
remedy this deficiency. Because of Joe, numerical transform inversion
and its application to analyze the performance of
complex systems has become one of my main research interests.
When we met, Joe had already been
using numerical transform inversion for 20 years.
Our numerical transform inversion work builds on Joe's long experience,
as can be seen from his seminal paper,
H. Dubner and J. Abate, "Numerical inversion of Laplace transforms by relating
them to the finite Fourier cosine transform."
J. ACM, vol. 15, 1968, pp. 115123.
For a quick introduction to basic algorithms
for numerically inverting Laplace transforms, see:
Numerical Inversion of Laplace Transforms of Probability Distributions.
ORSA Journal on Computing, vol. 7, 1995, pp. 3643.
[published PDF]
For a recent introduction and survey of our work on numerical transform inversion, see:
An Introduction to Numerical Transform Inversion and its Application to Probability Models, in
Computational Probability, W. Grassman (ed.), Kluwer, Boston, 1999, pp. 257323
(with Gagan L. Choudhury).
[PostScript]
[PDF]
(Books have been started.)
For papers that capture some of Joe's interesting perspective, see:
An Operational Calculus for Probability Distributions Via Laplace Transforms.
Advances in Applied Probability,
vol. 28, 1996, pp. 75113.
[published PDF]
Computing Laplace Transforms for Numerical Inversion Via Continued Fractions.
INFORMS Journal on Computing, vol. 11, No. 4, Fall 1999, pp. 394405.
[published PDF]
Address:
Joseph Abate, 900 Hammond Road, Ridgewood, NJ 074502908,
Fax: 2014470477
Here are our joint papers in chronological order:

Transient Behavior of the M/M/1 Queue: Starting at the Origin.
Queueing Systems: Theory and Applications,
vol. 2, No. 1, 1987, pp. 4165.
[published PDF]

Transient Behavior of Regulated Brownian Motion I: Starting at the Origin.
Advances in Applied Probability, vol. 19, No. 3, September 1987,
pp. 560598.
[published PDF]

Transient Behavior of Regulated Brownian Motion, II: NonZero Initial Conditions.
Advances in Applied Probability,
vol. 19, No. 3, September 1987, pp. 599631.
[published PDF]

Transient Behavior of the M/M/1 Queue Via Laplace Transforms.
Advances in Applied Probability,
vol. 20, No. 1, March 1988, pp. 145178.
[published PDF]

The Correlation Functions of RBM and M/M/1.
Stochastic Models,
vol. 4, No. 2, 1988, pp. 315359.
[published PDF]

Approximations for the M/M/1 Busy Period.
Queueing Theory and its Applications, Liber Amicorum for Professor J. W. Cohen
NorthHolland, Amsterdam, 1988, pp. 149191
[published PDF]

Simple Spectral Representations for the M/M/1 Queue.
Queueing Systems, vol. 3, No. 4, 1988, pp. 321346.
[published PDF]

Spectral Theory for SkipFree Markov Chains.
Probability in the Engineering and Information Sciences, vol. 3, No. 1, 1989, pp. 7788.
[published PDF]

Calculating TimeDependent Performance Measures for the M/M/1 Queue.
IEEE Transactions on Communications, vol. 37, No. 10, 1989, pp. 11021104.
[published PDF]

Decompositions of the M/M/1 Transition Function.
Queueing Systems, vol. 9, No. 3, 1991, & pp. 323336.
[published PDF]

The FourierSeries Method for Inverting Transforms of Probability
Distributions.
Queueing Systems, vol. 10, No. 1, 1992, pp. 588.
[published PDF]

Numerical Inversion of Probability Generating Functions.
Operations Research Letters, vol. 12, No. 4, 1992, pp. 245251.
[published PDF]

Solving Probability Transform Functional Equations for Numerical Inversion.
Operations Research Letters, vol. 12, 1992, pp. 275281.
[published PDF]

Calculation of the GI/G/1 steadyState WaitingTime Distribution and its Cumulants from Pollaczek's Formula.
Archiv für Elektronik und Übertragungstechnik,
vol. 47, No. 5/6, 1993, pp. 311321
(with Gagan L. Choudhury).
[published PDF]

Asymptotics for SteadyState Tail Probabilities in Structured Markov Queueing Models.
Stochastic Models, vol. 10, No. 1, 1994, pp. 99143
(with Joseph Abate and Gagan L. Choudhury).
[published PDF]

WaitingTime Tail Probabilities in Queues with LongTail ServiceTime Distributions.
Queueing Systems, vol. 16, 1994, pp. 311338
(with Joseph Abate and Gagan L. Choudhury).
[published PDF]

Transient Behavior of the M/G/1 Workload Process.
Operations Research, vol. 42, No. 4, 1994, pp. 750764.
[published PDF]

A HeavyTraffic Expansion for the Asymptotic Decay Rates of Tail Probabilities
in MultiChannel Queues.
Operations Research Letters, vol. 15, 1994, pp. 223230.
[PostScript]
[PDF]

Numerical Inversion of Laplace Transforms of Probability Distributions.
ORSA Journal on Computing, vol. 7, 1995, pp. 3643.
[published PDF]

Exponential Approximations for Tail
Probabilities in Queues, I:
Waiting Times.
Operations Research, vol. 43, 1995, pp. 885901
(with Joseph Abate and Gagan L. Choudhury).
[published PDF]

Limits and Approximations for the BusyPeriod Distribution in SingleServer Queues.
Probability in the Engineering and Informational Sciences,
vol. 9, 1995, pp. 581602. (with Joseph Abate)
[published PDF]

Calculating the M/G/1 BusyPeriod Density and the LIFO WaitingTime
Distribution by Direct Numerical Transform Inversion.
Operations Research Letters,
vol. 18, 1995, pp. 113119 (with Joseph Abate and Gagan L. Choudhury).
[published PDF]

Asymptotic Analysis of Tail Probabilities Based on the
Computation of Moments.
Annals of Applied Probability,
vol. 5, 1995, pp. 9831007
(with Joseph Abate, Gagan L. Choudhury and David M. Lucantoni).
[published PDF]

An Operational Calculus for Probability Distributions Via Laplace Transforms.
Advances in Applied Probability,
vol. 28, 1996, pp. 75113.
[published PDF]

Exponential Approximations for Tail Probabilities in Queues, II: Sojourn Time and Workload.
Operations Research, vol. 44, 1996, pp. 758763
(with Gagan L. Choudhury).
[published PDF]

On the Laguerre Method for Numerically Inverting Laplace
Transforms.
INFORMS Journal on Computing,
vol. 8, 1996, pp. 413427
(with Joseph Abate and Gagan L. Choudhury).
[published PDF]

Asymptotics for M/G/1 LowPriority WaitingTime Tail Probabilities.
Proceedings of 34th Allerton Conference on Communication, Control and Computing,
S. P. Meyn and W. K. Jenkins (eds.) 1996, pp. 923931.

Asymptotics for M/G/1 LowPriority WaitingTime Tail Probabilities.
Queueing Systems, vol. 25, 1997, pp. 173223.
[published PDF]

Limits and Approximations for the M/G/1 LIFO WaitingTime Distribution.
Operations Research Letters, vol. 20, 1997, pp. 199206.
[published PDF]

Numerical Inversion of Multidimensional Laplace Transforms by the Laguerre Method.
Performance Evaluation, vol. 31, 1998, pp. 229243
(with Gagan L. Choudhury).
[published PDF]

Calculating Transient Characteristics of the Erlang Loss Model by
Numerical Transform Inversion.
Stochastic Models, vol. 14, No. 3, 1998, pp. 663680. (with Joseph Abate)
[PDF]
[published PDF]

Modeling ServiceTime Distributions with NonExponential Tails: Beta Mixtures
of Exponentials.
Stochastic Models, vol. 15, No. 3, 1999, pp. 517546. (with Joseph Abate)
[PDF]
[published PDF]

Explicit M/G/1 WaitingTime Distributions for a Class of LongTail ServiceTime Distributions.
Operations Research Letters, vol. 25, No. 1, August 1999, pp. 2531.
[published PDF]

An Introduction to Numerical Transform Inversion and its Application to Probability Models, in
Computational Probability, W. Grassman (ed.), Kluwer, Boston, 1999, pp. 257323
(with Gagan L. Choudhury).
[PostScript]
[PDF]

InfiniteSeries Representations of Laplace Transforms of Probability Density Functions for Numerical Inversion.
Journal of Operations Research Society of Japan, vol. 42, No. 3,
September 1999, pp. 268285.
[published PDF]

Computing Laplace Transforms for Numerical Inversion Via Continued Fractions.
INFORMS Journal on Computing, vol. 11, No. 4, Fall 1999, pp. 394405.
[published PDF]

A Unified Framework for Numerically Inverting Laplace Transforms..
INFORMS Journal on Computing, vol. 18, No. 4, 2006, pp. 408421.
[PDF]

Integer Sequences from Queueing Theory.
Journal of Integer Sequences, vol. 13, 2010, article 10.5.5.
[PDF]

Brownian Motion and the Generalized Catalan Numbers..
Journal of Integer Sequences, under review.
[PDF]