Today, two of my female doctoral students, Sara Saberi and Dong "Michelle" Li, and the PI on our joint NSF grant, Professor Tilman Wolf, and I finished a paper: A Dynamic Network Economic Model of a Service-Oriented Internet with Price and Quality Competition, for the Network Models in Economics and Finance conference volume, Athens, Greece, edited by Professors Bautin, Rassias, and Pardalos, Springer, Berlin, Germany.
This research, was motivated, in part, by the Future Generation Internet(FGI), which will need to handle a spectrum of requirements of next-generation applications. In our model, both content providers and transport network providers have, as their strategic variables, the prices that they charge and their quality levels. And, in the paper, in order to model the quality of transport network service, we make use of the Kleinrock function, so that the greater the demand at higher quality, the larger the amount of bandwidth used.
And, just in time, the August 2013 edition of IEEE Computer magazine arrived at our door, which has a fabulous interview with none other than Dr. Leonard "Len" Kleinrock of UCLA, conducted by Charles Severance. The full interview, Computing Conversations, is online and I watched it this morning.
Dr. Kleinrock is a recipient of the National Medal of Science and numerous other awards. He is also an INFORMS Fellow, for the OR/MS geeks out there.
In the interview (and hardcopy article of its highlights) Kleinrock speaks of how he needed to make a mathematical simplifying assumption of independence in order to make his queuing model of round-robin time-slicing for data communications in order to protect short messages from waiting behind very long ones now called "packet switching" tractable. This was his PhD project at MIT under the renowned Claude Shannon. Then he was worried as to whether the assumption skewed the theoretical results, in which case they might not be useful in practice (and he would not get his PhD). So, Kleinrock built simulation software (this was back in the early 1960s) which consisted of a 2,500 line assembly language program.
I, honestly, had a deja vu experience and remembered my first project in industry, writing AN/UYK assembly language code to assist in submarine transiting -- something I have written about.
He ran the code, tested it with and without the simplifying assumption, and the results were "amazingly close."
He received his PhD in 1962 and McGraw-Hill published his dissertation as the book, Communication Nets: Stochastic Message Flow and Design, in 1964: ISBN 978-0486611051.
He noted in the interview that the book was a clear road map as to how to build the scalable shared wired and wireless networks we take for granted today... all that was needed was to get to work and build a network.
And then, according to Kleinrock: But nobody cared. I went to AT&T, the biggest network of the time, and explained: "You guys ought to give us good data communications." The answer was, "What are you talking about?...and, finally, "Little boy, go away." And so little boy went away and with others developed this technology that ate AT&T's lunch.
Lincoln Labs supported him for his Master's and PhD and then, when he was expected to return there to work, was told that he should explore other options -- very generous of Lincoln Labs.
I am forever grateful to both Systems Consultants and Aquidneck Data Corporation in Rhode Island for supporting me while I pursued my Master's in Applied Math from Brown University (and also worked full-time and ran marathons). One of my projects at the latter was developing queuing models for local area networks of different topologies.
Kleinrock's application for a position at UCBerkeley was lost because there was a switch in chairmen but a professor on sabbatical at MIT suggested UCLA and he has been there for 50 years!
His enthusiasm and wisdom shine through in his interview, and, at the very beginning, he even talks about planning to have his first child in 1958 -- how nice and thoughtful of him.
More info on Kleinrock can be found here.