Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers

In an important class of systems, which arises in manufacturing, chemical process, and computer contexts, objects move sequentially from one work station to another, and rest between stations in buffers. In the manufacturing context, such systems are called transfer lines. The dynamic behavior of a buffered transfer line with unreliable work stations is modeled as a Markov chain. The system states consist of the operational conditions of the work stations and the levels of material in the buffers. The steady-state probabilities of these states are sought in order to establish relationships between system parameters and performance measures such as production rate (efficiency), forced-down times, and expected in-process inventory. The steady state probabilities are found by choosing a sum-of-products form solution for a class of states, and deriving the remaining expressions by using the transition equations. In this way, the order of the system of equations to be solved is drastically reduced. This algorithm suggests a general approach for solving large scale structured Markov chain problems.