A solvable simplified model for elevator group control studies

We describe in some detail the technique of using a simplified model of a complex discrete dynamic system, in our case an elevator group control system, as a benchmark for control and optimization studies. The simplified system is constructed in a way that balances between two conflicting requirements: it retains the most important dynamical characteristics of the target system; but at the same time it allows exact solution by algorithmic methods. As a concrete example, we show the derivation of the "S-ring" model from a formal model of elevator group supervisory control, describe the solution process, and illustrate using the exact solution to benchmark some optimization methods. We also describe one variant, the "S-lane" model, and show its solution, as an example of extending the technique to related other problems.