Reddit mentions of Introduction to Probability Models

For undergrad probability, Pitman's book or Ross's two books here and here.

For graduate probability, Billingsley (h/t /u/DCI_John_Luther), Williams or Durrett.

Probability Models by Sheldon Ross: find this book, somehow! It's one of the best probability books I've ever read and has a thorough treatment of Markov Chains as they would relate to anyone in modeling (e.g. econometrics, business, OM, etc.). It's easy to read, a good balance of rigor and conventional explanations, great examples, intuitive, and great problem sets. I highly recommend it.

http://www.amazon.com/Introduction-Probability-Models-Tenth-Edition/dp/0123756863

I think this book by Ross is the standard advanced undergraduate text that gives a nice introduction to the subject. In my school it was the text used for a probability 2 course, and is also pretty well known around actuary circles. Its not a bad read for self study and I think the material is decent. It is expensive, but I see this book everywhere so it shouldn't be difficult for you to find a cheap copy. If anyone has a better introduction, do tell.