Learn basic probability theory. Purchase or borrow a book that focuses on introducing the student to the basics of probability theory. You do not need to brush up on other types of math, as probability theory only assumes a basis in basic algebra and arithmetic.
Read deeply on the Poisson distribution, the basis of Poisson processes. The Poisson distribution is a mathematical model that describes rare events, such as typos on a page or earthquakes. It is a mathematical function that describes the probabilities of the occurrences of such events. Familiarize yourself with the Poisson distribution’s mathematical form -- memorize it. Know when to use it to model situations. Practice applying the Poisson distribution to word problems (your book should have at least one set of these problems).
Solidify your knowledge of probability theory. Take the in-book exams on the units that focus on probability distributions and applying probability distributions. If your book has an advanced section on the Poisson distribution, read it (such a section will likely be titled “Poisson processes”).
Purchase or borrow a book on queuing theory. Read the sections on Poisson processes and Markov chains first. Markov chains are mathematical flowchart-like maps that describe the likelihood of certain events leading to other events. Markov chains usually appear in the form of matrices, so it is best if you review basic matrix theory before studying this subject. After learning the fundamentals of these mathematical processes, learn how these processes represent lines.
Learn how to calculate the limiting distribution for line models. Books on queuing theory or Markov chains will contain chapters on this topic. Practice finding the limiting distribution for Markov chains given in the book.
Learn how to analyze the limiting distribution in terms of strengths and weaknesses. Recall that the limiting distribution represents the long-term evaluation of a line. Understand that you can only accurately analyze a line by looking at it from a long-term standpoint. Know that the criteria for line strength or weakness commonly includes line design efficiency, average time spent in a line for a given customer and use of resources for the line system.
Begin applying what you have learned to your career or real-life lines. Set up a mathematical model for a line in your business or computer system. Apply the analytical methods you have learned through studying queuing theory. Make conclusions based on the limiting distributions of the lines.