[dvas]

I would recommend a guided series of lectures to get started with and then pick up a book or lectures pdf's once you are comfortable with the basics to expand.

In my opinion, there is a bit of a cliff of learning, where the beginning starts out harder, then begin the application of the theory. Others have mentioned, Little's Law, Erlang model, Kendall's notation etc..

Starting to learn, I would look at the following (since subject matter experts can explain the concepts and analogies much better):

    * MAP6264 Queueing Theory, Prof. Robert B. Cooper.
      https://www.youtube.com/watch?v=AsTuNP0N7DU

    * MIT OCW, 15.072J | Spring 2006 | Graduate
    * Queues: Theory And Applications.
      https://ocw.mit.edu/courses/15-072j-queues-theory-and-applications-spring-2006/

For books, performance engineering/benchmarking topics usually contain a refresher on the basics and application of queuing theory which I think makes it easy to see its use.

To answer your question regarding one book to start with:

    * An Introduction to Queueing Systems by Sanjay K.Bose

    * Slides for Lectures Based on the Book
    http://home.iitk.ac.in/~skb/ee679/ee679.html

    * Sample tests and solutions
    http://home.iitk.ac.in/~skb/qbook/sample_tests.html