What good are models?

Abstract

Models are central to engineering. They are used for analysis, synthesis, and communication between humans. A given artifact or process may have multiple models with different purposes, modeling different aspects, or modeling at varying levels of abstraction. In this paper, we give a general overview of how models are used, with the goal of making the concepts clearer for different communities. We focus on the domain of track-based flow management of automated systems, and identify two different modeling styles, Eulerian and Lagrangian. Eulerian models focus on regions of space, whereas Lagrangian models focus on entities moving through space. We discuss how the features of the system, like having centralized or decentralized control or the ability to install fixed infrastructure, influence the choice between these styles. Although the choice between modeling styles is rarely made consciously, it affects modeling efficiency, and one style may be far better suited for certain modeling problems than another. For problems with a more global nature concerning the physical space, an Eulerian model is likely to be a better match. For problems that concern the moving objects specifically, where the identity of the individual objects is important, a Lagrangian view is the one to choose. In many cases, combining the two styles is the most effective approach. We illustrate the two styles using an example of an automated quarry.