Diffusion approximations for three-stage transfer lines with unreliable machines and finite buffers

In this paper, we derive an approximate model for the flow of parts in a three-stage transfer line with unreliable machines and finite storage elements. The analysis of exact models of these systems was described in Gershwin and Schick [1], where the basic notation for this paper is established. In [1], it was noted that exact analysis of three-stage or higher problems is very difficult, if not altogether impossible. In this paper we develop an approximation methodology which is used to study the three-stage transfer line model. This methodology can be extended to n-stage transfer lines without introducing additional levels of complexity. These extensions are discussed in [2].