HeavyTraffic Limits and Diffusion Approximations for One Queue

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).
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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.

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/∞ Queues.
Advances in Applied Probability, vol. 14, No. 1,
March 1982, pp. 171190.

Refining Diffusion Approximations for
Queues.
Operations Research Letters,
vol. 1, No. 5, November 1982, pp. 165169.

Heavy Traffic Approximations
for Service Systems with Blocking.
AT&T Bell Laboratories Technical Journal, vol. 63, No. 4, MayJune 1984, pp. 689708.

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.

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.
[PostScript]
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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).

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).

Unstable Asymptotics for Nonstationary Queues.
Mathematics of Operations Research, vol. 19,
No. 2, 1994, pp. 267291 (with William A. Massey).
[PostScript]
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PiecewiseLinear Diffusion Processes.
Advances in Queueing, J. Dshalalow, ed., CRC Press,
Boca Raton, FL, 1995, pp. 463480 (with Sid Browne).
[PostScript]
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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).
[PostScript]
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HeavyTraffic ExtremeValue Limits for Queues.
Operations Research Letters,
vol. 18, 1995, pp. 107111
(with Peter W. Glynn).
[PostScript]
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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).
[PostScript]
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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 L. Choudhury, Avi Mandelbaum and Martin I. Reiman).
[PostScript]
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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).
[PostScript]
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Periodic Load Balancing.
Queueing Systems, vol. 30, Nos. 12, 1998, pp. 203250
(with Gísli Hjálmtýsson).
[PostScript]
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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.
[PostScript]
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Limits for Cumulative Input Processes to Queues.
Probability in the Engineering and Information Sciences,
vol. 14, 2000, pp. 123150.
[PostScript]
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How multiserver queues scale with growing congestiondependent
demand.
Submitted to Operations Research.
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