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Transient State Analysis of Queue-Size Behavior and Throughput of the Manufacturing Line with Finite Buffer Capacity and Machine Setup and Closedown Times

A single machine queuing system with setup/closedown times generally distributed is considered. Production tasks enter the production system with exponentially distributed interarrival times and are served by times assumed to be generally distributed. Arriving production tasks form a single waiting line and are served in the order of their arrivals. A production task is stored in a finite-capacity buffer if it arrives and the machine is busy or setup activities are done. Whenever a production system is empty, the machine is stopped by a closedown time. The machine needs a setup time before providing the service of the first task after the idle time.