Ward Whitt

Heavy-Traffic 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. 150-177 (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. 355-369 (with Donald L. Iglehart). [published PDF]
Multiple Channel Queues in Heavy Traffic III: Random Server Selection. Advances in Applied Probability, vol. 2, No. 2, Autumn 1970, pp. 370-375.
Weak Convergence Theorems for Priority Queues: Preemptive-Resume Discipline. Journal of Applied Probability, vol. 8, No. 1, March 1971, pp. 74-94. [published PDF]
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. 1372-1378 (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. 185-191.
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, Springer-Verlag, New York, 1974, pp. 307-350. [published PDF]
Some Useful Functions for Functional Limit Theorems. Mathematics of Operations Research, vol. 5, No. 1, February 1980, pp. 67-85. [published PDF]
Heavy-Traffic Limits for Queues with Many Exponential Servers. Operations Research, vol. 29, No. 3, May-June 1981, pp. 567-588 (with Shlomo Halfin). [published PDF]
On the Heavy-Traffic Limit Theorem For GI/G/infinity Queues. Advances in Applied Probability, vol. 14, No. 1, March 1982, pp. 171-190. [published PDF]
Refining Diffusion Approximations for Queues. Operations Research Letters, vol. 1, No. 5, November 1982, pp. 165-169.
Departures from a Queue with Many Busy Servers. Mathematics of Operations Research, Vol. 9, No. 4, November 1984, pp. 534-544.
Heavy Traffic Approximations for Service Systems with Blocking. AT&T Bell Laboratories Technical Journal, vol. 63, No. 4, May-June 1984, pp. 689-708. [published PDF]
Queues with Superposition Arrival Processes in Heavy Traffic. Stochastic Processes and Their Applications, vol. 21, No. 1, December 1985, pp. 81-91.
Book Review: Asymptotic Methods in Queueing Theory by A. A. Borovkov (translated by D. Newton), Wiley, 1984. American Scientist, vol. 75, No. 2, March-April 1987, pp. 210-211.
Transient Behavior of Regulated Brownian Motion I: Starting at the Origin. Advances in Applied Probability, vol. 19, No. 3, September 1987, pp. 560-598 (with Joseph Abate). [published PDF]
Transient Behavior of Regulated Brownian Motion, II: Non-Zero Initial Conditions. Advances in Applied Probability, vol. 19, No. 3, September 1987, pp. 599-631 (with Joseph Abate). [published PDF]
Transient Behavior of the M/M/1 Queue Via Laplace Transforms. Advances in Applied Probability, vol. 20, No. 1, March 1988, pp. 145-178 (with Joseph Abate).
The Correlation Functions of RBM and M/M/1. Stochastic Models, vol. 4, No. 2, 1988, & pp. 315-359 (with Joseph Abate).
Simple Spectral Representations for the M/M/1 Queue. Queueing Systems, vol. 3, No. 4, 1988, pp. 321-346 (with Joseph Abate).
An Interpolation Approximation for the Mean Workload in a GI/G/1 Queue. Operations Research, vol. 37, No. 6, 1989, pp. 936-952.
Dependence in Packet Queues: A Multi-Class Batch-Poisson Model. Teletraffic Science for New Cost-Effective Systems, Networks and Services, Proceedings of ITC 12, (ed. M. Bonatti), North-Holland, Amsterdam, 1989, pp. 1450-1454 (with Kerry W. Fendick and Vikram R. Saksena).
Dependence in Packet Queues. IEEE Transactions on Communications, vol. 37, No. 11, 1989, pp. 1173-1183 (with Kerry W. Fendick and Vikram R. Saksena). [published PDF]
Planning Queueing Simulations. Management Science, vol. 35, No. 11, 1989, pp. 1341-1366. [published PDF]
Simulation Run Length Planning. 1989 Winter Simulation Conference Proceedings, pp. 106-112. [PostScript] [PDF]
Queues with Service Times and Interarrival Times Depending Linearly and Randomly Upon Waiting Times. Queueing Systems , vol. 6, No. 4, 1990, pp. 335-351.
Diffusion Approximations for Queues with Server Vacations. Advances in Applied Probability, vol. 22, No. 3, 1990, pp. 706-729. (with Offer Kella) [published PDF]
The Heavy-Traffic Bottleneck Phenomenon in Open Queueing Networks. Operations Research Letters, vol. 9, No. 6, 1990, pp. 355-362 (with S. Suresh). [published PDF]
Departures from Many Queues in Series. Annals of Applied Probability, vol. 1, No. 4, 1991, pp. 546-572 (with Peter W. Glynn). [PDF]
A New View of the Heavy-Traffic Limit for Infinite-Server Queues. Advances in Applied Probability, vol. 23, No. 1, 1991, pp. 188-209 (with Peter W. Glynn).
The Brownian Approximation for Rate-Control Throttles and the G/G/1/C Queue. Journal of Discrete Event Dynamic Systems, vol. 2, No. 1, 1992, pp. 7-60 (with Arthur W. Berger).
Large Fluctuations in a Deterministic Multiclass Network of Queues, Management Science, vol. 39, No. 8, 1993, pp. 1020-1028. [publishedPDF]
Diffusion Approximations for Open Queueing Networks with Service Interruptions. Queueing Systems, vol. 13, No. 4, 1993, pp. 335-359 (with Hong Chen).
Heavy-Traffic 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. 129-136. (with Gagan L. Choudhury).
Heavy-Traffic Asymptotic Expansions for the Asymptotic Decay Rates in the BMAP/G/1 Queue. Stochastic Models, vol. 10, No. 2, 1994, pp. 453-498 (with Gagan L. Choudhury). [PostScript] [PDF]
A Heavy-Traffic Expansion for the Asymptotic Decay Rates of Tail Probabilities in Multi-Channel Queues. Operations Research Letters, vol. 15, 1994, pp. 223-230 (with Joseph Abate). [PostScript] [PDF]
Towards Better Multi-Class Parametric-Decomposition Approximations for Open Queueing Networks. Annals of Operations Research, vol. 48, 1994, pp. 221-248. [PostScript] [PDF]
Unstable Asymptotics for Nonstationary Queues. Mathematics of Operations Research, vol. 19, No. 2, 1994, pp. 267-291 (with William A. Massey). [PostScript] [PDF]
Piecewise-Linear Diffusion Processes. Advances in Queueing, J. Dshalalow, ed., CRC Press, Boca Raton, FL, 1995, pp. 463-480 (with Sid Browne). [published PDF]
Maximum Values in Queueing Processes. Probability in the Engineering and Informational Sciences, vol. 9, 1995, pp. 375-409 (with Arthur W. Berger). [PostScript] [PDF]
Heavy-Traffic Extreme-Value Limits for Queues. Operations Research Letters, vol. 18, 1995, pp. 107-111 (with Peter W. Glynn). [PostScript] [PDF]
Limits and Approximations for the Busy-Period Distribution in Single-Server Queues. Probability in the Engineering and Informational Sciences, vol. 9, 1995, pp. 581-602 (with Joseph Abate). [PostScript] [PDF]
Fluid and Diffusion Limits for Queues in Slowly Changing Random Environments. Stochastic Models, vol. 13, No. 1, 1997, pp. 121-146 (with Gagan Choudhury, Avishai Mandelbaum and Martin I. Reiman). [published PDF]
Limits and Approximations for the M/G/1 LIFO Waiting-Time Distribution. Operations Research Letters, vol. 20, 1997, pp. 199-206 (with Joseph Abate). [PostScript] [PDF]
Periodic Load Balancing. Queueing Systems, vol. 30, Nos. 1-2, 1998, pp. 203-250 (with Gísli Hjálmtýsson). [published PDF]
Approximations for Periodic Load Balancing. 37th IEEE Conference on Decision and Control, Tampa, Florida (with Gísli Hjálmtýsson).
An Overview of Brownian and Non-Brownian FCLTs for Single-Server Queues. Queueing Systems, vol. 36, 2000, pp. 39-70. [PostScript] [PDF] [published PDF]
Limits for Cumulative Input Processes to Queues. Probability in the Engineering and Information Sciences, vol. 14, 2000, pp. 123-150. [PostScript] [PDF]
The Reflection Map with Discontinuities. Mathematics of Operations Research, vol. 26, No. 3, 2001, pp. 447-484. [PostScript] [PDF]
BOOK: Stochastic-Process 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 Congestion-Dependent Demand. Operations Research, vol. 51, No. 4, 2003, pp. 531-542. [publishedPDF]
Heavy-Traffic Limits for Loss Proportions in Single-Server Queues. Queueing Systems, vol. 46, No. 3-4, March-April 2004, pp. 507-536. [publishedPDF]
A Diffusion Approximation for the G/GI/n/m Queue. Operations Research, vol. 52, No. 6, November-December 2004, pp. 922-941. [publishedPDF]
Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments. Management Science, vol. 50, No. 10, October 2004, pp. 1449-1461. [PDF] [published PDF]
Heavy-Traffic Limits for the G/H2*/n/m Queue. Mathematics of Operations Research, vol. 30, No. 1, February 2005, pp. 1-27. [published PDF]
Fluid Models for Many-Server Queues with Abandonments. Operations Research, forthcoming. [PDF]
Two Fluid Approximations for Multi-Server Queues with Abandonments. Operations Research Letters, vol. 33, 2005, pp. 363-372. [PDF][published PDF]

Related topics:

Large Deviation Limits and Tail Probability Asymptotics