In this study, we propose some simple but effective throughput-approximation methods for finite-buffered closed-loop production systems with unreliable machines and exponentially distributed processing times. The proposed approximation methods are based on decomposition and aggregation principles. According to the method representing the decomposed systems, three different approximation methods are developed, along with a simple upper bounding method for throughputs. Extensive computational experiments are performed to show the effectiveness of the approximation and upper bounding methods.
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