Effect of buffer size on productivity of work stations that are subject to breakdown

A production line consisting of two work stations in series, and intermediate buffer of size m is modeled as a discrete-parameter Markov process with 4m + 8 states. Owing to the block structure of the transition probability matrix, the steady-state probabilities are obtained by the successive solution of systems of 4 simultaneous equations. Moreover, the probabilities of the interior states are shown to follow a scalar geometric relation Hence numerical solutions are very easily obtained even for large buffer sizes. An empirical formula for the production rate is presented. This formula is remarkably accurate over a wide range of parameters.