The throughput rate of three-station production lines: a unifying solution

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Abstract
A three-station production line with a Laplace transformable distribution of service time of the middle station and phase-type distribution of service times of the two outside stations is treated. A general formula for the throughput rate is derived. In this formula a system of linear equations with the number of equations equal to the number of stages of the service time of the last station needs to be solved. For some special cases, this formula reduces to simple expressions.

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