Analysis of Departure Times in Discrete and Continuous Tandem Production Lines

We study the departure times in tandem production lines where the products passing through the lines are either discrete entities or continuous fluid. We call these discrete tandem (DT) or continuous tandem (CT) lines, respectively. We apply sample path analysis techniques to relate the departure time in a DT line to the departure time in a CT line where both lines have equivalent model parameters. We show that the departure time of a quantity q, produced at a machine in a DT line governed by the communication blocking mechanism, converges to the departure time of the same quantity at the same machine in the corresponding CT line as the size of the products in the DT line becomes infinitesimally small. Since continuous fluid models are used in both queueing and control systems to approximate the behavior of discrete systems, this asymptotic result enhances the understanding and the use of such models. Finally, our result also leads to an alternative proof for the convexity of the departure time in CT lines.