Publications with Gagan L. Choudhury
Collaboration with
Gagan L. Choudhury began in 1992
when he spent a year as an intern in the
Mathematics of Networks and Systems Department
(headed by Debasis Mitra, where I was) in the Mathematical Sciences
Research Center at Bell Labs. As a member of the Network Design and Performance
Analysis Department (headed by
Pat Wirth),
Gagan had already established a strong interest in algorithms and
performance analysis tools. Thus Gagan was an ideal
person to partner with Joe Abate and me
in our efforts to develop numerical transform inversion tools.
Gagasn is now a Lead Member of Technical Staff in the "Optimization, Reliability and Customer Analytics" Department of AT&T Labs research.
He was named a Fellow if the IEEE in 2009.
Gagan was especially attracted to hard problems. Thus he
was attracted to the challenging multidimensional numerical transform
inversion problems. Indeed, Gagan wrote almost all the
multidimensional inversion code. In doing so, Gagan
demonstrated extraordinary algorithm and programming skills as well as
mastery of the underlying theory.
The basic multidimensional numerical transform
inversion algorithms are not so difficult (when the
dimension is not large), as can be
seen from our 1994
Annals of Applied Probability
paper. The real difficulty usually lies in
developing special methods to treat specific problems.
The challenge, and Gagan's great contribution, can be seen
by looking at the 1995 J. ACM paper
on closed queueing networks, the 1995 ToN paper
on stochastic loss networks with statedependent rates,
the 1996 Performance Evaluation paper on polling
systems and the 1997 Operations Research paper
on the M_{t}G_{t}/1 queue (all appearing below). The
algorithms in those papers go well beyond a direct application of
the multidimensional inversion algorithm.
In addition to his important direct personal contributions,
Gagan also has helped
expand the numericalinversion project by helping to enlist the cooperation
of outstanding colleagues from his
department such as
David Lucantoni and
Kin Leung.
Gagan also contributed greatly to technology
transfer within AT&T by leading the development of the
"Qsquared" numericalinversionbased performance analysis
tool in his department.
For an introduction and survey 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 Joseph Abate).
[PostScript]
[PDF]
Here are all papers coauthored with Gagan in chronological order:

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 JosephAbate).
[published PDF]

HeavyTraffic Asymptotic Expansions for the Asymptotic Decay Rates
in the BMAP/G/1 Queue.
Proceedings of the ITC Seminar on Teletraffic Analysis Methods
for Current and Future Telecom Networks,
Bangalore, India, November 1993, pp. 129136.

Computing Transient Distributions in General SingleServer Queues.
Proceedings of IEEE Globecom 93,
No. 29.1, 1993, pp. 10451050 (with David M. Lucantoni).
[published PDF]

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

The Transient BMAP/G/1 Queue.
Stochastic Models, vol. 10, No. 1, 1994, pp. 145182 (with Gagan L. Choudhury and David M. Lucantoni).
[published PDF]

HeavyTraffic Asymptotic Expansions for the Asymptotic Decay Rates in
the & BMAP/G/1 Queue.
Stochastic Models, vol. 10, No. 2, 1994,
pp. 453498. (with Gagan L. Choudhury)
[published PDF]

On the Effectiveness of Effective Bandwidths for
Admission Control in ATM Networks.
The Fundamental Role of Teletraffic in the Evolution of
Telecommunications Networks, Proceedings of the 14th International Teletraffic Congress,
J. Labetoulle and J. W. Roberts (eds.), Elsevier, Amsterdam,
vol. 1a, 1994, pp. 411420 (with David M. Lucantoni).

Numerical Transform Inversion to Analyze Teletraffic Models.
The Fundamental Role of Teletraffic in the Evolution of
Telecommunications Networks, Proceedings of the 14th International Teletraffic Congress,
J. Labetoulle and J. W. Roberts (eds.), Elsevier, Amsterdam,
vol. 1b, 1994, 10431052 (with David M. Lucantoni).
[PostScript]
[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]

MultiDimensional Transform Inversion with Applications to the Transient M/G/1 Queue.
Annals of Applied Probability
vol. 4, 1994, pp. 719740
(with David M. Lucantoni).
[published PDF]

An Algorithm for Closed Queueing Networks Based on Numerical Transform Inversion.
Proceedings of the 1994 Conference on Information Science and Systems,
ed. H. Kobayashi, Department of Electrical Engineering, Princeton
University, pp. 711 (with Kin K. Leung).
[PostScript]
[PDF]

An Algorithm for ProductForm Loss Networks Based on Numerical Inversion of
Generating
Functions.
Proceedings IEEE Globecom `94, 1994, pp. 11231128 (with Kin K. Leung).
[published PDF]

An Algorithm to Compute Blocking Probabilities in MultiRate MultiClass
MultiResource Loss Models.
ComputerAided Modeling, Analysis and Design
of Communication Links and Networks, 1994 (CAMAD '94, 1994, (with Gagan L. Choudhury).
[published PDF]

ResourceSharing Models with StateDependent Arrivals of Batches.
Computations with Markov Chains,
W. J. Stewart, ed., Kluwer, Boston,
1995, pp. 255282 (with Kin K. Leung).
[published PDF]

Q^{2}: A New Performance Analysis Tool Exploiting Numerical Transform
Inversion.
Proceedings of Third International Workshop on Modeling, Analysis and
Simulation of Computer and Telecommunication Systems,
(MASCOTS `95), Durham, NC, January 1995, pp. 411415.
[PostScript]
[PDF]
[published PDF]

An Inversion Algorithm for Loss Networks with State Dependent Rates.
Proceedings of IEEE Infocom `95,
1995, pp. 513521 (with Kin K. Leung).
[published PDF]

Computing Transient and SteadyState Distributions in Polling Models
by Numerical Transform Inversion.
IEEE International Conference on Communications,
Seattle, WA, June 1995, pp. 803809.
[PDF file from IEEE]
[published PDF]

Calculating Normalization Constants of Closed Queueing Networks by Numerically Inverting
Their Generating Functions.
Journal of the Association for Computing Machinery, vol. 42,
1995, pp. 935970 (with Kin K. Leung).
[PostScript]
[PDF]
From ACM Digital Library.

Efficiently Providing Multiple Grades of Service with Protection
Against Overloads in Shared Resources.
AT&T Technical Journal,
vol. 74, No. 4, 1995, pp. 5063 (with Gagan L. Choudhury and Kin K. Leung).
[published PDF]

An Inversion Algorithm to Calculate Blocking Probabilities in Loss Networks
with StateDependent Rates.
IEEE/ACM Transactions on Networking,
vol. 3, No. 5, 1995, pp. 585601 (with Gagan L. Choudhury and Kin K. Leung).
[ published PDF]

Exponential Approximations for Tail
Probabilities in Queues, I:
Waiting Times.
Operations Research, vol. 43, 1995, pp. 885901
(with JosephAbate).
[published PDF]

An Algorithm to Calculate Blocking Probabilities in MultiRate MultiClass
MultiResource Loss Models.
Advances in Applied Probability, vol. 27, 1995,
pp. 11041143 (with Kin K. Leung).
[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).
[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 and David M. Lucantoni).
[published PDF]

Squeezing the Most Out of ATM.
IEEE Transactions on Communications,
vol. 44, No. 2, 1996, pp. 203217 (with David M. Lucantoni).
[PostScript]
[PDF]
[published PDF]

Computing Distributions and Moments in Polling Models by Numerical Transform Inversion.
Performance Evaluation,
vol. 25, No. 4, 1996, pp. 267292
(with Gagan L. Choudhury).
[published PDF]

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

Fluid and Diffusion Limits for Queues in Slowly Changing Random Environments.
Stochastic Models,
vol. 13, No. 1, 1997, pp. 121146 (with Gagan Choudhury, Avishai Mandelbaum and Martin I. Reiman).
[published PDF]

Numerical Solution of PiecewiseStationary M_{t}/G_{t}/1 Queues.
Operations Research, vol.~45, No.~3, 1997, pp. 451463,(with Gagan L. Choudhury and David M. Lucantoni).
[published PDF]

Scaling for Numerical Transform Inversion to Analyze Teletraffic Models.
Teletraffic Contributions for the Information Age, Proceedings
of ITC 15, V. Ramaswami and P. E. Wirth
(eds.), Elsevier,
Amsterdam, 1997, pp. 933942.

Probabilistic Scaling for the Numerical Inversion of
NonProbability Transforms.
INFORMS Journal on Computing,
vol. 9, No. 2, 1997, pp. 175184.
[PDF]
[published PDF]

LongTail BufferContent Distributions in Broadband Networks.
Performance Evaluation, Vol. 30, 1997, pp. 177190.
[published PDF]

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

Efficiently Providing Multiple Grades of Service with Protection
Against Overloads in Shared
Resources,
U.S. patent 5,719,854 issued February 17, 1998 (with Kin K. Leung).

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