Studies on Systems with Random Disruptions via Fluid Models

Motivated by studing manufacturing systems in which job arrival and processing times are essentially deterministic but the environment is typically random, we develop a fluid network model with random disruptions, and show that it is a functional strong law of large numbers limit of the corresponding queueing network model. Conditions for the existence of limiting and stationary distributions are also established. The usefulness of the model is further illustrated through a pathwise bound (between the queueing and the fluid inventory processes), and some simple, explicit results for stationary distributions in the single-station case, obtained via standard results in random walk theory.