Transient analysis of Bernoulli serial lines: performance evaluation and system-theoretic properties

Transient behavior of production systems has significant practical and theoretical implications. However, analytical methods for analysis and control of production systems during transients remain largely unexplored. In the framework of serial production lines with Bernoulli machines and finite buffers, this article develops a mathematical model for transient analysis and derives closed-form expressions for evaluating the production rate, consumption rate, work-in-process, and probabilities of machine starvation and blockage during transients. In addition, a computationally efficient procedure based on recursive aggregation is developed to approximate the transient performance measures with high accuracy. Finally, based on the mathematical model derived, system-theoretic properties of several important system transient characteristics are studied.