Performance modelling and Markov chains

Markov chains have become an accepted technique for modeling a great variety of situations. They have been in use since the early 1900's, but it is only in recent years with the advent of high speed computers and cheap memory that they have begun to be applied to large-scale modeling projects. This paper outlines the events that have lead to the present state-of-the-art in the numerical approach to Markov chain performance modeling and describes current solution methods and ongoing research efforts.