Which is a good introductory book for Markov chains and Markov processes?
Theory of Markov Processes by Eugene Dynkin is a paperback published by Dover, so it has the advantage of being inexpensive. The author has made many contributions to the subject. Dynkin’s lemma, the Dynkin diagram and the Dynkin system are named after him.
“An Introduction to Stochastic Modeling” by Karlin and Taylor is a very good introduction to Stochastic processes in general. Bulk of the book is dedicated to Markov Chain. This book is more of applied Markov Chains than Theoretical development of Markov Chains. This book is one of my favorites especially when it comes to applied Stochastics.
An Introduction to Markov Chain Analysis and An Introduction to Markov Processes would be a good start.
A foundational paper is :
An Introduction to Hidden Markov Models – Rabiner 1986
which explains the processes from first principles which is sadly rare on academic papers.
Allen, Arnold O.: “Probability, Statistics, and Queueing Theory with Computer Science Applications”, Academic Press, Inc., San Diego, 1990 (second Edition)
This is a very good book including some chapters about Markov chains, Markov processes and queueing theory.