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 African-Americans take advantage of the opportunities such as have been provided by the Bell Labs Cooperative Research Fellowship Program. Bill is a co-founder and leading organizer of the Conferences for African-American 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 time-dependent arrival rates, especially infinite-server ``offered-load'' models. Bill has been working on queues with time-dependent arrival rates since his 1981 thesis with Joseph B. Keller at Stanford. Together, Bill and I have concentrated on offered-load models. The offered-load 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 offered-load models, it is often possible to develop tractable mathematical descriptions that capture the important time-varying rate of customer demand. Since offered loads are so much easier to analyze than carried loads, offered-load models are very promising for engineering capacity-planning studies. The idea is to design to meet projected customer demand based on offered-load models. Often the uncertainty about future demand greatly exceeds the error caused by using offered-load models instead of carried-load models. There are significant applications of offered-load models to wireless networks, private-line service, the Internet and telephone call centers.

Here are my papers with Bill in chronological order:

  1. The Physics of The Mt/G/infty Queue. Operations Research, vol. 41, No. 4, 1993, pp. 731-742 (with Stephen G. Eick). [published PDF]
  2. Mt/G/infty Queues with Sinusoidal Arrival Rates. Management Science, vol. 39, No. 2, 1993, pp. 241-252 (with Stephen G. Eick). [published PDF]
  3. Networks of Infinite-Server Queues with Nonstationary Poisson Input. Queueing Systems, vol. 13, No. 1, 1993, pp. 183-250. [published PDF]
  4. A Probabilistic Generalization of Taylor's Theorem. Statistics and Probability Letters, vol. 16, No. 1, 1993, pp. 51-54. [published PDF]
  5. The Highway PALM: A Stochastic Model to Capture Space and Time Dynamics in Wireless Communication Systems. Proceedings of the Thirty-First Annual Allerton Conference on Communication, Control and Computing, University of Illinois, September 1993, pp. 859-867.
  6. Unstable Asymptotics for Nonstationary Queues. Mathematics of Operations Research, vol. 19, No. 2, 1994, pp. 267-291. [PostScript] [PDF]
  7. On the Modified-Offered-Load 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. 145-154.
  8. 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. 503-512.
  9. Traffic Models for Wireless Communication Networks. IEEE Infocom `94 Proceedings, IEEE Computer Society Press, 1994, pp. 1029-1037 (with Kin K. Leung and William A. Massey). [published PDF]
  10. Traffic Models for Wireless Communication Networks. IEEE Journal on Selected Areas in Communication, vol. 12, No. 8, 1994, pp. 1353-1364 (with Kin K. Leung and William A. Massey). [published PDF]
  11. A Stochastic Model to Capture Space and Time Dynamics in Wireless Communication Systems. Probability in the Engineering and Informational Sciences, vol. 8, 1994, pp. 541-569. [PDF]
  12. An Analysis of the Modified Offered Load Approximation for the Nonstationary Erlang Loss Model. Annals of Applied Probability, vol. 4, 1994, pp. 1145-1160. (with William A. Massey) [published PDF]
  13. Sensitivity to the Service-Time Distribution in the Nonstationary Erlang Loss Model. Management Science, vol. 41, No. 6, 1995, pp. 1107-1116 (with Jimmie L. Davis and Bill Massey). [published PDF]
  14. Estimating the Parameters of a Nonhomogeneous Poisson Process with Linear Rate. Telecommunication Systems, vol. 5, 1996, pp. 361-388 (with Geraldine A. Parker). [published PDF]
  15. Server Staffing to Meet Time-Varying Demand. Management Science, vol. 42, No. 10, 1996, pp. 1383-1394 (with Otis B. Jennings and Avishai Mandelbaum). [published PDF]
  16. Stationary-Process Approximations for the Nonstationary Erlang Loss Model. Operations Research, vol. 44, 1996, pp. 976-983. [published PDF]
  17. The Time-Dependent Erlang Loss Model with Retrials. Proceedings of INFORMS Telecommunications Conference, Telecommunications Systems, R. B. Cooperand and R. Doverspike (eds.), vol. 7, 1997, pp. 253-265 (with Nathaniel Grier and Tyrone McKoy). [PostScript] [PDF] [published PDF]
  18. Peak Congestion in Multi-Server Service Systems with Slowly Varying Arrival Rates. Queueing Systems, vol. 25, 1997, pp. 157-172. [published PDF]
  19. Applications of the Infinite-Server Queue to the Management of Private Line Services. Proceedings of 1997 AT&T Services and Infrastructure Symposium (SIPS-97), Middletown, NJ, November 18-19, 1997, pp. 132-141 (with Clement A. McCalla).
  20. Uniform Acceleration Expansions for Markov Chains with Time-Varying Rates. Annals of Applied Probability, vol. 9, No. 4, 1998. (with William A. Massey) [published PDF]
  21. Method for Determining Server Staffing in Management of Finite Server Queueing Systems. U.S. Patent 5,923,873 issued July 13, 1999.
  22. A Nonstationary Offered-Load Model for Packet Networks. Telecommunication Systems, vol. 13, Nos. 3,4, March-April 2001, pp. 271-296 (with Nicholas G. Duffield). [PostScript] [PDF] [published PDF]
  23. Staffing of Time-Varying Queues to Achieve Time-Stable Performance. Management Science, vol. 54, No.2, February 2008, pp. 324-338. (with Zohar Feldman, Avishai Mandelbaum and William A. Massey). [PDF].