Analytic methods for calculating performance measures of production lines with buffer storages

A Markov Chain model of an unreliable transfer line with interstage buffer storages is introduced. The system states are defined as the operational conditions of the stages and the levels of material in the storages. 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. A matrix solution that exploits the sparsity and block tri-diagonal structure of the transition matrix is discussed. The steady-state probabilities of the system states are also found analytically, by guessing a sum-of-products form solution for a class of states and deriving the remaining expressions by using the transition equations.