Approximation analysis for some arbitrary configurations of production systems using decomposition

Production systems consisting of unreliable machines and finite buffers, which can be modeled as networks with arbitrary configuration, are considered in this paper. The performance of such systems is highly influenced by the failures of machines and the fluctuations in processing times. The effects of these factors can be reduced by the use of buffers, which temporarily hold in-process inventories. In this paper, an efficient analytical approximation method is developed using decomposition for modeling and analyzing these production systems. The results of the expected steady state throughput rates obtained using the analytical approximation method are compared with simulation results. The analytical approximation method works very efficiently and satisfactorily, giving results with an acceptable error level.