Publications with William A. Massey
Collaboration with
Bill Massey
began in 1987 when I joined the
Mathematics of Networks and Systems Department
in the
Mathematical Sciences Research Center of Bell Labs (now part of Lucent
Technologies),
first headed by Jim McKenna and then
Debasis Mitra.
(See the
list of
former members.) See Bill's more complete earlier
Bell Labs web page.
Bill had received his A.B. and Ph.D. degrees in mathematics
from Princeton in 1977 and Stanford in 1981, which partly explains Bill's fondness
for communicating with chalk at the blackboard, and why Bill's mind is quite
a bit better organized than his office. Bill attended
graduate school with the support of a Bell Labs Cooperative Research Fellowship.
Immediately upon receiving his Ph.D. from Stanford, Bill returned to
Bell Labs, where he remained until 2001. In 2001 he joined
the Department of Operations Research and Financial Engineering at Princeton.
In addition to pursuing his
research interests in probability theory and its applications, Bill
has been very active in mentoring, helping other AfricanAmericans take advantage of the
opportunities such as have been provided by
the Bell Labs Cooperative Research Fellowship Program.
Bill is a cofounder and leading organizer
of the Conferences for AfricanAmerican Researchers in the Mathematical
Sciences (CAARMS). which provides a forum for
current and future African American researchers
in the mathematical sciences and showcases their work. For example, Bill helped organize
their
sixth annual conference held in June 2000,
their
seventh annual conference held in June 2001
and their
eighth annual conference to be held in Princeton in June 2002. Bill is a leading
mathematician
of the African diaspora
in the spirit of David
Blackwell.
My research collaboration with Bill has focused on
queueing models with timedependent arrival rates, especially infiniteserver
``offeredload'' models.
Bill has been working on queues with timedependent arrival rates
since his 1981 thesis with
Joseph B. Keller
at Stanford. Together, Bill and I have concentrated on offeredload models.
The offeredload models descibe the load that would be on the
system if there were no limit to the available resources.
It is much easier to
describe the offered load than the carried load, which must reflect
loss and delay, due to limited resources. Indeed, for the offeredload
models, it is often possible to develop tractable mathematical
descriptions that capture the important timevarying rate of
customer demand.
Since offered loads are so much easier to analyze than carried loads,
offeredload models are very promising for engineering capacityplanning studies.
The idea is to design to meet projected customer demand based on offeredload models.
Often the uncertainty about future demand greatly exceeds the error caused
by using offeredload models instead of carriedload models.
There are significant applications of offeredload models to wireless networks,
privateline service, the Internet and telephone call centers.
Here are my papers with Bill in chronological order:

The Physics of The M_{t}/G/infty Queue.
Operations Research, vol. 41, No. 4, 1993, pp. 731742
(with Stephen G. Eick).
[published PDF]

M_{t}/G/infty
Queues with Sinusoidal Arrival Rates.
Management Science, vol. 39, No. 2, 1993,
pp. 241252 (with Stephen G. Eick).
[published PDF]

Networks of InfiniteServer Queues with Nonstationary Poisson Input.
Queueing Systems, vol. 13, No. 1, 1993, pp. 183250.
[published PDF]

A Probabilistic Generalization of Taylor's Theorem.
Statistics and Probability Letters, vol. 16,
No. 1, 1993, pp. 5154.
[published PDF]

The Highway PALM: A Stochastic Model to Capture Space and Time Dynamics in Wireless Communication Systems.
Proceedings of the ThirtyFirst Annual Allerton Conference on Communication, Control and Computing,
University of Illinois,
September 1993, pp. 859867.

Unstable Asymptotics for Nonstationary Queues.
Mathematics of Operations Research, vol. 19, No. 2, 1994, pp. 267291.
[PostScript]
[PDF]

On the ModifiedOfferedLoad Approximation for the Nonstationary Erlang Loss Model.
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. 145154.

The Highway PALM: A Stochastic Model to Capture Space and Time
Dynamics in Wireless Communication Systems.
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. 503512.

Traffic Models for Wireless Communication Networks.
IEEE Infocom `94 Proceedings, IEEE Computer Society Press,
1994, pp. 10291037
(with Kin K. Leung and William A. Massey).
[published PDF]

Traffic Models for Wireless Communication Networks.
IEEE Journal on Selected Areas in Communication, vol. 12, No. 8, 1994,
pp. 13531364
(with Kin K. Leung and William A. Massey).
[published PDF]

A Stochastic Model to Capture Space and Time Dynamics in Wireless Communication Systems.
Probability in the Engineering and Informational Sciences,
vol. 8, 1994, pp. 541569.
[PDF]

An Analysis of the Modified Offered Load Approximation for the Nonstationary Erlang Loss Model.
Annals of Applied Probability, vol. 4, 1994, pp. 11451160. (with William A. Massey)
[published PDF]

Sensitivity to the ServiceTime Distribution in the Nonstationary Erlang Loss Model.
Management Science, vol. 41, No. 6, 1995, pp. 11071116 (with Jimmie L. Davis and Bill Massey).
[published PDF]

Estimating the Parameters of a Nonhomogeneous Poisson Process with Linear Rate.
Telecommunication Systems,
vol. 5, 1996, pp. 361388
(with Geraldine A. Parker).
[published PDF]

Server Staffing to Meet TimeVarying Demand.
Management Science,
vol. 42, No. 10, 1996, pp. 13831394
(with Otis B. Jennings and Avishai Mandelbaum).
[published PDF]

StationaryProcess Approximations for the Nonstationary Erlang Loss Model.
Operations Research, vol. 44, 1996, pp. 976983.
[published PDF]

The TimeDependent Erlang Loss Model with Retrials.
Proceedings of INFORMS Telecommunications Conference, Telecommunications Systems,
R. B. Cooperand and R. Doverspike (eds.), vol. 7, 1997, pp. 253265 (with Nathaniel Grier and Tyrone McKoy).
[PostScript]
[PDF]
[published PDF]

Peak Congestion in MultiServer Service Systems with Slowly Varying Arrival Rates.
Queueing Systems, vol. 25, 1997, pp. 157172.
[published PDF]

Applications of the InfiniteServer Queue to the Management of
Private Line Services.
Proceedings of 1997 AT&T Services and Infrastructure Symposium (SIPS97), Middletown, NJ, November 1819, 1997, pp. 132141
(with Clement A. McCalla).

Uniform Acceleration Expansions for Markov Chains with TimeVarying Rates.
Annals of Applied Probability, vol. 9, No. 4, 1998. (with William A. Massey)
[published PDF]

Method for Determining Server Staffing in Management of Finite Server Queueing Systems.
U.S. Patent 5,923,873 issued July 13, 1999.

A Nonstationary OfferedLoad Model for Packet Networks.
Telecommunication Systems,
vol. 13, Nos. 3,4, MarchApril 2001, pp. 271296 (with Nicholas G. Duffield).
[PostScript]
[PDF]
[published PDF]

Staffing of TimeVarying Queues to Achieve
TimeStable Performance.
Management Science, vol. 54, No.2, February 2008, pp. 324338. (with Zohar Feldman, Avishai Mandelbaum and William A. Massey).
[PDF].

Staffing of TimeVarying Queues to Achieve
TimeStable Performance, Unabridged Version:
Internet Supplement.
working paper, 2005.
(with Zohar Feldman, Avishai Mandelbaum and Bill Massey)
[PDF].