Alan Weiss

A few months after I began working at Bell Labs, NJ in 1981, I went on a trip to Bell Labs in Naperville, IL, where a group was doing innovative work on packet networks. A visiting professor from Italy told me that there was a key problem in packet traffic modeling: how large should the buffers be to get extremely low overflow probabilities? This was an interesting question. I immediately put aside my other work and training, and began learning large deviations. Fortunately, my dissertation adviser, S. R. S. Varadhan, was and is the premier researcher in the theory of large deviations. I went to him regularly for advice.

Within a few years I had learned enough to publish my first paper in the field (1986). I took a sabbatical at the University of Maryland and taught a course on applications of large deviations. Afterward, I tried to turn the lecture notes into a book. I failed for several years.

Eventually I enlisted Adam Shwartz of the Technion to help me turn my rough, incomplete notes into a complete, readable book, with proofs and examples. In the process, Adam and I became close friends, and our families spent a good deal of time together. I hope the results of our work show our love of the subject, and enable you to understand this rather technical area.