Tuesday, April 15, 2008

Books from my Shelf, Part 2

Continuing a list of some interesting books...

Reversibility and Stochastic Networks, Frank Kelly: This was the book that got me interested in queueing theory style mathematics -- well, really it was a course I took from Frank Kelly, based on the book, and Frank then gave me a copy. The book is out of print, but nicely available online from the link. It's all about Markov chains, queues, queueing networks, and various applications. While I'm sure there are more "modern" treatments, I think the book holds up quite nicely.

Queueing Systems (Volume 1, Theory), Leonard Kleinrock: Another classic with all the basics of queueing theory, including all the fundamental results of all the basic types of queues. (While Volume 2, on Computer Applications, is also interesting, I think Volume 1 is much more useful.)

A First Course in Stochastic Processes, Karlin and Taylor: OK, another classic probability book. (Yes, there's still more of them to come.) Markov chains, renewal theory, Brownian motion, branching processes, etc. (While the Second Course, with more advanced material, is also interesting and useful, I think the first book is much more important.)

Introduction to Probability Theory and Its Applications (vols 1 and 2), Feller. Again with the classics. The classics are apparently classics for a reason, at least in my mind...

4 comments:

Isabel Lugo said...

I recently read (I wish I could remember where) that all mathematicians who study probability have read Feller but very few of them will actually admit to it because it's a rather concrete book and admitting that one likes to see actual examples is seen as a sign of weakness.

I am, perhaps, one of those mathematicians.

Anonymous said...

Yes, I also enjoyed Karlin-Taylor when I was a grad student. Also, you perhaps know that Prof. Samuel Karlin (Anna Karlin's father) passed away a few months ago.

aravind

Andy D said...

I'm curious to know what the set 'queueing theory style mathematics' contains, besides queueing theory, and what its challenges and rewards are...

Michael Mitzenmacher said...

Aravind -- yes, I had heard about Samuel passing away. A great loss. He's another one of those people that when you look at the span of his career, and the variety of things he has done, it's quite inspirational.

Andy -- queueing theory style mathematics is much "continuous-oriented" than I think most CS people are used to. A lot of arguments based on flow in = flow out, or the limit has to equal the right value, where CS people might want to make things more precise (and complicated, without necessarily gaining more insight) by discretizing everything. I don't think it's less rigorous, it's just that continuous intuitions are more accepted and understood.