Sample Path Analysis for Continuous Tandem Production Lines

We consider a tandem production line where the product flowing through the line is continuous fluid. We call such a line a continuous tandem (CT) line. We derive a recursive representation for the departure time of products in CT lines. Next, we apply sample path analysis techniques to prove that the departure time is convex (in the sense of strong stochastic convexity) in the flow rates of the machines. We then prove that the infinitesimal perturbation analysis (IPA) estimate, for the gradient of throughput with respect to machine flow rates, is strongly consistent.