Frank P. Kelly

It is with great pleasure that the INFORMS Committee for the Expository Writing Award names Frank P. Kelly, Professor of the Mathematics of Systems at the University of Cambridge, as the recipient of its 2013 award.  A Fellow of Britain’s Royal Society and Commander of the Order of the British Empire, Professor Kelly’s seminal research - in the theory of stochastic networks, and applications of this theory to the design and control of communications systems - has been recognized with many prior awards, including the INFORMS Lanchester and von Neumann prizes.  The present award celebrates the excellence of Professor Kelly’s expository writing. 

Professor Kelly’s book Reversibility and Stochastic Networks, first published in 1979 and subsequently reprinted in 1987, 1994 and 2011, has been cited more than 2,500 times. In this work, Professor Kelly succinctly and elegantly developed the concepts of reversibility and quasi-reversibility, and explained how they simplify the analysis of many stochastic networks.  While the exposition is rigorous, even the most advanced sections are accessible to readers with only a basic knowledge of probability theory. Also of note are the many thought-provoking exercises at the end of each section, for writing good exercises is hard. One published review states that “The book is truly well written… elegant and intellectually stimulating without being unnecessarily general or abstract…In clarity, generality, and elegance there is no close competitor,”¹ while a second reviewer reports that “Part of the reason the mathematics is so clear is that Kelly's pleasant, simple English exploits fully the power of natural language to describe abstract processes.”² Those who read this book are unlikely to forget Professor Kelly’s initial description of reversibility: “Speaking intuitively, if we take a film of such a process and then run the film backwards the resulting process will be statistically indistinguishable from the original process.”

Professor Kelly has also authored or coauthored roughly 100 articles that contribute to the literature in many different areas, including stochastic networks, queueing theory, communication networks, population biology, search theory, transportation, and group decision-making. To highlight one example, Professor Kelly’s most-cited paper, “Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability” (co-authored with AK Maulloo and DKH Tan,Journal of the Operational Research Society, 1998), has been referenced nearly 4,250 times. Building upon his earlier work, this article joins stability, an engineering issue, with fairness, an economic issue, in developing tractable models for allocating flow rates across the users of a communication network. The authors provide decentralized schemes by which a network can manage itself, and the resulting bandwidth allocations have the property that the amount a user is willing to pay is equal to the amount charged by the network. As appropriate for an article modeling communications traffic, the writing “flows” through the paper’s structural “nodes” of problem description, model formulation, theoretical analysis and numerical examples.  It is an exciting paper to read. 

Professor Kelly’s exposition is careful, patient, and clear. His work exemplifies the art of technical writing, and has been extremely influential in both theory and applications.  For these reasons, the Expository Writing Committee (Edward H. Kaplan, Robert A. Shumsky and Dimitris Bertsimas) is pleased to name Frank P. Kelly as the recipient of the 2013 INFORMS Expository Writing Award.

¹Networks13(1):153-154; 1983.
²Technometrics23(2):206-207; 1981.

The 2008 John von Neumann Theory Prize is awarded by the Institute for Operations Research and the Management Sciences to Frank Kelly for his profound contributions to the mathematical theory of stochastic networks, and for applications of these theories to the understanding, performance evaluation, and design of telecommunications networks.

Early in his career, Frank Kelly developed important modeling extensions to the theory of product-form queueing networks that was pioneered by J. R. Jackson, a class of network models that offer closed-form solutions for their steady-state distributions. In addition, he introduced the concept of a quasireversible station and showed that when a network is comprised of quasireversibile stations, then product-form behavior for that network follows. This body of theory also provided a clear explanation, based on the notion of a “symmetric queueing discipline”, for the phenomenon known as “insensitivity” that describes those queueing models whose steady-state distributions depend on the associated service requirement distributions only through their means.

Of equal impact was his study of a class of loss networks known as circuit-switched networks, in an asymptotic regime in which the link capacity grows in proportion to the rate at which calls are placed on each of the routes that are served by the network. In this very natural and well-motivated asymptotic regime, one finds that the equilibrium distribution can asymptotically be characterized as the solution of an optimization problem, with blocking across each link that occurs independently. He then went on to develop and analyze dynamic alternative routing strategies for telephone networks in a set of papers that has both influenced call routing strategies worldwide and that led to a scheme that has been implemented in some digital telephone networks.

His recent work has been guided by the need to develop theoretical tools for the analysis of the Internet, and has focused largely on the understanding of self-regulation in large-scale systems. In particular, his mathematical framework, based on principles of dual decomposition, for implementing congestion control and fair resource allocation through distributed pricing schemes has greatly influenced the networking community.

Kelly is a Fellow of the Royal Society and has previously been awarded the Rollo Davidson Prize, the Lanchester Prize, the Naylor Prize, and the Kobayashi Prize. He also served as Chief Scientific Advisor to the United Kingdom Department for Transport from 2003 to 2006.

Award presented by Jim Dai, Committee Member, and Cynthia Barnhart, President, October 12, 2008.

Frank P. Kelly of the Statistical Laboratory at the University of Cambridge, England, was named the 1991 winner of the Lanchester Prize for his paper, "Loss Networks," The Annals of Applied Probability.

The award citation reads in part: "In a series of six major papers ... published during 1985-91 culminating in the survey paper, 'Loss Networks,' Frank P. Kelly has taken the leap from the theory of Erlang which aptly described the village telephone exchange of 1917, to a theory that is fully capable of the analysis of today's global telecommunications network ... This work of Frank P. Kelly is highly original, has very important applications, contains deep theoretical insights of great mathematical beauty and makes an important contribution to the field of operations research."