HeavyTraffic Limits and Diffusion Approximations for Queues

Weak Convergence Theorems for Queues in Heavy Traffic. Ph.D. Thesis, Cornell University January 1969.

Multiple Channel Queues in Heavy Traffic I.
Advances in Applied Probability,
vol. 2, No. 1, Spring 1970, pp. 150177 (with Donald L. Iglehart).

Multiple Channel Queues in Heavy Traffic II: Sequences, Networks, and Batches. Advances in Applied Probability,
vol. 2, No. 2, Autumn 1970, pp. 355369 (with Donald L. Iglehart).
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Multiple Channel Queues in Heavy Traffic III: Random Server Selection.
Advances in Applied Probability, vol. 2, No. 2, Autumn 1970, pp. 370375.

Weak Convergence Theorems for Priority Queues: PreemptiveResume Discipline.
Journal of Applied Probability, vol. 8, No. 1, March 1971, pp. 7494.
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The Equivalence of Functional Central Limit Theorems for Counting Processes and Associated Partial Sums.
Annals of Mathematical Statistics, vol. 42, No. 4, August 1971,
pp. 13721378 (with Donald L. Iglehart).

Complements to Heavy Traffic Limit Theorems for the GI/G/1 Queue.
Journal of Applied Probability, vol. 9, No. 1, March 1972, pp. 185191.

Heavy Traffic Limit Theorems for Queues: A Survey.
Mathematical Methods in Queueing Theory,
Proceedings of a Conference at Western Michigan University, Lecture Notes in
Economics and Mathematical Systems, No. 98, SpringerVerlag, New York, 1974, pp. 307350.
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Some Useful Functions for Functional Limit Theorems.
Mathematics of Operations Research,
vol. 5, No. 1, February 1980, pp. 6785.
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HeavyTraffic Limits for Queues with
Many Exponential Servers.
Operations Research, vol. 29, No. 3, MayJune 1981,
pp. 567588 (with Shlomo Halfin).
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On the HeavyTraffic Limit Theorem
For GI/G/infinity Queues.
Advances in Applied Probability, vol. 14, No. 1,
March 1982, pp. 171190.
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Refining Diffusion Approximations for
Queues.
Operations Research Letters,
vol. 1, No. 5, November 1982, pp. 165169.

Departures from a Queue with Many Busy
Servers.
Mathematics of Operations Research, Vol. 9,
No. 4, November 1984, pp. 534544.

Heavy Traffic Approximations
for Service Systems with Blocking.
AT&T Bell Laboratories Technical Journal, vol. 63, No. 4, MayJune 1984, pp. 689708.
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Queues with Superposition Arrival Processes in Heavy Traffic.
Stochastic Processes and Their Applications,
vol. 21, No. 1, December 1985, pp. 8191.

Book Review: Asymptotic Methods in Queueing Theory
by A. A. Borovkov (translated by D. Newton), Wiley, 1984.
American Scientist, vol. 75, No. 2, MarchApril 1987, pp. 210211.

Transient Behavior of Regulated Brownian Motion I:
Starting at the Origin.
Advances in Applied Probability, vol. 19, No. 3, September 1987,
pp. 560598 (with Joseph Abate).
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Transient Behavior of Regulated Brownian Motion, II: NonZero
Initial Conditions.
Advances in Applied Probability,
vol. 19, No. 3, September 1987, pp. 599631
(with Joseph Abate).
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Transient Behavior of the M/M/1 Queue Via Laplace Transforms.
Advances in Applied Probability,
vol. 20, No. 1, March 1988, pp. 145178 (with Joseph Abate).

The Correlation Functions of RBM and M/M/1.
Stochastic Models,
vol. 4, No. 2, 1988, & pp. 315359 (with Joseph Abate).

Simple Spectral Representations for the M/M/1 Queue.
Queueing Systems, vol. 3, No. 4, 1988, pp. 321346 (with Joseph Abate).

An Interpolation Approximation for the Mean Workload in a GI/G/1 Queue.
Operations Research, vol. 37, No. 6, 1989, pp. 936952.

Dependence in Packet Queues: A MultiClass BatchPoisson Model.
Teletraffic Science for New CostEffective Systems, Networks and Services,
Proceedings of ITC 12, (ed. M. Bonatti), NorthHolland,
Amsterdam, 1989, pp. 14501454 (with Kerry W. Fendick and Vikram R. Saksena).

Dependence in Packet Queues.
IEEE Transactions on Communications,
vol. 37, No. 11, 1989, pp. 11731183
(with Kerry W. Fendick and Vikram R. Saksena).
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Planning Queueing Simulations.
Management Science, vol. 35, No. 11, 1989, pp. 13411366.
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Simulation Run Length Planning.
1989 Winter Simulation Conference Proceedings, pp. 106112.
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Queues with Service Times and Interarrival Times Depending Linearly and
Randomly Upon Waiting Times.
Queueing Systems , vol. 6, No. 4, 1990, pp. 335351.

Diffusion Approximations for Queues with Server Vacations.
Advances in Applied Probability,
vol. 22, No. 3, 1990, pp. 706729. (with Offer Kella)
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The HeavyTraffic Bottleneck Phenomenon in Open Queueing Networks.
Operations Research Letters, vol. 9, No. 6, 1990, pp. 355362
(with S. Suresh).
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Departures from Many Queues in Series.
Annals of Applied Probability, vol. 1, No. 4, 1991, pp. 546572 (with Peter W. Glynn).
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A New View of the HeavyTraffic Limit for InfiniteServer Queues.
Advances in Applied Probability, vol. 23, No. 1, 1991, pp. 188209 (with Peter W. Glynn).

The Brownian Approximation for RateControl Throttles and
the G/G/1/C Queue.
Journal of Discrete Event Dynamic Systems, vol. 2, No. 1, 1992, pp. 760 (with Arthur W. Berger).

Large Fluctuations in a Deterministic Multiclass Network of Queues,
Management Science, vol. 39, No. 8, 1993, pp. 10201028.
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Diffusion Approximations for Open Queueing Networks with Service Interruptions.
Queueing Systems, vol. 13, No. 4, 1993, pp. 335359 (with Hong Chen).

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. (with Gagan L. Choudhury).

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).
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A HeavyTraffic Expansion for the Asymptotic Decay Rates of Tail
Probabilities in MultiChannel Queues.
Operations Research Letters, vol. 15, 1994, pp. 223230
(with Joseph Abate).
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Towards Better MultiClass ParametricDecomposition Approximations for Open
Queueing Networks.
Annals of Operations Research,
vol. 48, 1994, pp. 221248.
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Unstable Asymptotics for Nonstationary Queues.
Mathematics of Operations Research, vol. 19,
No. 2, 1994, pp. 267291 (with William A. Massey).
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PiecewiseLinear Diffusion Processes.
Advances in Queueing, J. Dshalalow, ed., CRC Press,
Boca Raton, FL, 1995, pp. 463480 (with Sid Browne).
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Maximum Values in Queueing Processes.
Probability in the Engineering and Informational Sciences,
vol. 9, 1995, pp. 375409
(with Arthur W. Berger).
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HeavyTraffic ExtremeValue Limits for Queues.
Operations Research Letters,
vol. 18, 1995, pp. 107111
(with Peter W. Glynn).
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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).
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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).
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Limits and Approximations for the M/G/1 LIFO
WaitingTime Distribution.
Operations Research Letters, vol. 20, 1997, pp. 199206 (with Joseph Abate).
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Periodic Load Balancing.
Queueing Systems, vol. 30, Nos. 12, 1998, pp. 203250
(with Gísli Hjálmtýsson).
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Approximations for Periodic Load Balancing.
37th IEEE Conference on Decision and Control, Tampa, Florida
(with Gísli Hjálmtýsson).

An Overview of Brownian and NonBrownian FCLTs for SingleServer Queues.
Queueing Systems, vol. 36, 2000, pp. 3970.
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Limits for Cumulative Input Processes to Queues.
Probability in the Engineering and Information Sciences,
vol. 14, 2000, pp. 123150.
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The Reflection Map with Discontinuities.
Mathematics of Operations Research, vol. 26, No. 3, 2001,
pp. 447484.
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BOOK: StochasticProcess Limits, published by Springer in 2002 (602 pages).

Internet Supplement to the Book, published by Springer in 2002 (602 pages).

How Multiserver Queues Scale with Growing CongestionDependent Demand.
Operations Research, vol. 51, No. 4, 2003, pp. 531542.
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HeavyTraffic Limits for Loss Proportions
in SingleServer Queues.
Queueing Systems, vol. 46, No. 34, MarchApril 2004, pp. 507536.
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A Diffusion Approximation for the G/GI/n/m Queue.
Operations Research, vol. 52, No. 6, NovemberDecember 2004, pp. 922941.
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EfficiencyDriven HeavyTraffic Approximations
for ManyServer Queues with Abandonments.
Management Science, vol. 50, No. 10, October 2004, pp. 14491461.
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HeavyTraffic Limits for the G/H2*/n/m Queue.
Mathematics of Operations Research, vol. 30, No. 1, February 2005, pp. 127.
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Fluid Models for ManyServer Queues with Abandonments.
Operations Research, forthcoming.
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Two Fluid Approximations for MultiServer Queues with Abandonments.
Operations Research Letters, vol. 33, 2005, pp. 363372.
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