Collaborations with Arthur Berger started in the late 1980's while we both were at Bell Labs. Arthur joined Bell labs after completing his Ph.D. in applied mathematics and control theory at Harvard under the supervision of Professors Yu-Chi (Larry) Ho of Harvard and Fred C. Schweppe of M.I.T. Arthur's thesis focused on pricing mechanisms in coupled dynamic systems. In particular, Arthur investigated how pricing mechanisms can be used to control large systems when there are subsystems owned and operated by autonomous decision makers. The results are applied to electric utilities to study the feasibility of independently owned bulk power generation. Arthur's thesis remains of interest today, with the recent focus on pricing mechanisms to help manage the Internet. Shortly after joining Bell Labs, Arthur did work in a similar spirit, investigating game-theoretic pricing schemes for AT&T's shared private networks.

While at AT&T, Arthur was very active in standards bodies, serving as key U.S. delegate and associate rapporteur to the International Telecommunications Union (ITU) Study Groups 2 and 13 on B-ISDN traffic engineering and resource management. Arthur also represented AT&T at the ATM Forum and the U.S. standards body T1S1. What little I know about standards bodies is due to my association with Arthur. I always felt AT&T was fortunate to have Arthur in these positions, because he is one of the few mathematician/engineers I know who, I felt, could also have served in the foreign service as a diplomat.

Arthur is currently a senior research scientist at Akamai Technologies, working on the mapping of requests from web browsers to appropriate Akamai servers, and a research scientist in the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL).

The focus of my joint work with Arthur has been primarily on ways to manage and control communication networks, as can be seen from the nifty names in our papers: token-bank rate-control throttles, leaky buckets, sliding windows and effective bandwidths.

Here are our papers in chronological order:

1. A Multi-Class Input Regulation Throttle. Proceedings of the 29th IEEE Conference on Decision, and Control, December 1990, pp. 2106-2111. [published PDF]
2. 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. [published PDF].
3. Comparisons of Multi-Server Queues with Finite Waiting Rooms. Stochastic Models, vol. 8, No. 4, 1992, pp. 719-732. [published PDF].
4. The Impact of a Job Buffer in a Token-Bank Rate-Control Throttle. Stochastic Models, vol. 8, No. 4, 1992, pp. 685-717. [published PDF].
5. Efficient, Rate-Based Multiaccess Control, U.S. Patent No. 5,274,644 issued December 12, 1993 (with Rodolfo A. Milito).
6. The Pros and Cons of a Job Buffer in a Token-Bank Rate-Control Throttle. IEEE Transactions on Communications, vol. 42, No. 3, 1994, pp. 857-861. [published PDF]
7. Asymptotics for Open-Loop Window Flow Control. Journal of Applied Mathematics and Stochastic Analysis, special issue honoring L. Takàcs, vol. 7, 1994, pp. 337-356. [published PDF]
8. A Comparison of the Sliding Window and the Leaky Bucket. Queueing Systems, vol. 20, 1995, pp. 117-138. [published PDF].
9. Maximum Values in Queueing Processes. Probability in the Engineering and Informational Sciences, vol. 9, 1995, pp. 375-409. [PDF] [published PDF]
10. Extending the Effective-Bandwidth Concept to Networks with Priority Classes. IEEE Communications Magazine, vol. 36, No 8, August 1998, pp. 78-84. [published PDF]
11. Effective Bandwidths with Priorities. IEEE/ACM Transactions on Networking, vol. 6, No. 4, August 1998, pp. 447-460 (with Arthur W. Berger). [published PDF]
12. Traffic Management in Packet Communication Networks Having Service Priorities and Employing Effective Bandwidths, U.S. Patent 6,160,818 issued December 12, 2000.