Publications with Peter W. Glynn
Peter Glynn
and I have very similar backgrounds  only shifted in time
by a few (too many) years. After studying mathematics at Carleton University
in Ottawa, and doing an honors project on diffusion approximations
for queues with
Donald Dawson, Peter pursued graduate study in operations research
at
Stanford University.
At Stanford Peter wrote his thesis on simulation output
analysis for generalstatespace Markov chains, earning his Ph.D. in 1982.
Like me, Peter's dissertation advisor was
Donald Iglehart.
After teaching at Wisconsin for five years, Peter returned to Stanford to
be on the faculty, where he is today.
My interactions with Peter
began shortly
after he finished his thesis. At a conference he said that he had some ideas
about generalizing the famous conservation law L = W, also
known as
Little's law,
and applying the results
to simulation. I must have shown some flicker of recognition and appreciation.
In turn, no good deed should go unpunished.
Since there was a certain amount of devil in the details, that kept us both
busy for quite a while.
And one thing leads to another, as you can see below.
The focus of my research with Peter has been on asymptotics (primarily
functional central limit theorems)
that provide useful insight into queueing performance,
conservation laws such as L = W and ways to perform stochastic
simulations more efficiently. There is an interesting excursion into
hydrodynamic limits, stemming from our both being readers of
Raj Srinivasan's Ph.D. thesis with
Don Dawson at Carleton.

A CentralLimitTheorem Version of
L = W.
Queueing Systems: Theory and Applications, vol. 1, No. 2, September 1986, pp. 191215.
[published PDF]

Sufficient Conditions for Functional Limit
Theorem Versions of L = W.
Queueing Systems: Theory and Applications,
vol. 1, No. 3, 1987, pp. 279287.
[published PDF]

Ordinary CLT and WLLN Versions of L = W.
Mathematics of Operations Research, vol. 13, No. 4, 1988, pp. 674692.
[published PDF]

An LIL Version of L = W.
Mathematics of Operations Research, vol. 13, No. 4, 1988, pp. 693710.
[published PDF]

Indirect Estimation Via L = W.
Operations Research,
vol. 37, No. 1, 1989, pp. 82103.
[published PDF]

Extensions of the Queueing Relations
L = W and H = G.
Operations Research,
vol. 37, No. 4, 1989, pp. 634644.
[published PDF]

A New View of the HeavyTraffic Limit for InfiniteServer Queues.
Advances in Applied Probability, vol. 23, No. 1, 1991, pp. 188209.
[published PDF]

Departures from Many Queues in Series.
Annals of Applied Probability, vol. 1, No. 4, 1991, pp. 546572.
[published PDF]

Estimating the Asymptotic Variance with Batch Means.
Operations Research Letters, vol. 10, 1991, pp. 431435.
[PostScript]
[PDF]

The Asymptotic Validity of Sequential Stopping Rules in Stochastic
Simulations.
Annals of Applied Probability, vol. 2, No. 1, 1992, pp. 180198.
[published PDF]

The Asymptotic Efficiency of Simulation Estimators.
Operations Research, vol. 40, No. 3, 1992, pp. 505520.
[published PDF]

Estimating Customer and Time Averages.
Operations Research, vol. 41, No. 2, 1993, pp. 400408
(with Benjamin Melamed).
[published PDF]

Limit Theorems for Cumulative Processes.
Stochastic Processes and Their Applications, vol. 47,
1993, pp. 299314.
[published PDF]

Logarithmic Asymptotics for SteadyState Tail Probabilities in a SingleServer Queue.
Studies in Applied Probability, Papers
in Honour of Lajos Takàcs, J. Galambos and J. Gani (eds.), Applied
Probability Trust, Sheffield, England, 1994, pp. 131156.
[published PDF]

Large Deviations Behavior of Counting Processes and Their Inverses.
Queueing Systems, vol. 17,
1994, pp. 107128.
[published PDF]

HeavyTraffic ExtremeValue Limits for Queues.
Operations Research Letters,
vol. 18, 1995, pp. 107111.
[PDF]
[published PDF]

Winning the Hand of the Princess Saralinda.
Appied Probability and Stochastic Processes, Festschrift for
Julian Keilson, J. G. Shanthikumar and U. Sumita (eds.), Kluwer, Boston, 1999,
Chapter 16, pp. 231246
[PostScript]
[PDF]

Necessary Conditions in Limit Theorems for Cumulative Processes.
Stochastic Processes and Their Applications,
vol. 98, 2002, pp. 199209 (with Peter W. Glynn).
[published PDF]