Introduction to Cyclic Replacement Systems

Abstract

A fundamental and unified treatment of problems akin to the classical Swedish Machine Problem is presented. Section I describes the nature of the systems known as cyclic replacement systems. In Section II pertinent facts about Markov processes are gathered. In Section III, it is shown that a certain class of cyclic systems behave as homogeneous Markov processes. The special class of homogeneous Markov processes known as homogeneous birth and death processes is considered in Section IV. Results of Section IV are applied to some cyclic replacement systems in Section V. In Section VI some systems are treated which cannot be represented as birth and death processes.