Analysis of multistation production systems with limited buffer capacity .1. The subsystem model

We seek efficient techniques to evaluate the performance of multistation production systems with limited interstation buffers and station breakdown. Our ultimate objective is to develop a practical computer implementation that can be used for analysis and design. Practically implies two design considerations: flexibility and computational efficiency. The approach must be flexible enough to be applicable to production systems with various topologies and station characteristics. These include series arrangements of production systems, as well as network topologies and rework (feedback) systems. Similarly the technique must be computationally expedient. Our approach is based on a framework to model single-buffer subsystems to be used within a decomposition technique to evaluate the performance of the entire system. The first part presents a quasi-birth-death process model for the subsystems. Exploiting the spectral characteristics of the associated matrix polynomial, we develop a novel solution procedure for the steady-state probabilities where the computational effort is independent of the buffer size. The solution procedure is applicable to quasi birth-death processes. The efficient solution procedure developed in this part is used as a building block in decomposing and analyzing multistation production systems with various topologies in the second part of the study.