A decomposition method for the analysis of long buffered production systems with discrete general Markovian machines

This paper presents a new decomposition method for the approximate performance evaluation of buffered multi-stage production systems where machines are modeled as generally complex discrete time Markov chains with reward. The method is based on the exact solution of smaller two-machine sub-systems, also referred as building blocks, with machines that also feature such general characteristics. A decomposition approach is developed that propagates all the possible interruptions of flow due to starvation and blocking conditions throughout the pseudo-machines of each building block. In order to deal with such general settings, new decomposition equations are developed. A new algorithm is proposed for solving these decomposition equations. The proposed method proves to be very fast and accurate over a wide range of test cases, partly reported in this paper. To prove the generality of the framework, reported cases are focused on systems with generally distributed up and down times and systems with degrading machines. This method paves the way to the analysis of a wider class of previously un-investigated systems. © IFAC.