We ran one billion agents . Scaling in simulation models

We provide a clarification of scaling issues in simulation models, distinguishing between sample size determination, discovery of emergent properties involving a qualitative change in the behaviour of the system at an aggregate level, and ‘true’ scaling, the dependence of the quantitative behaviour of the system at any given level of aggregation, to its size. Scaling issues arise because we want to understand what happens when we run one billion agents, without actually having to run one billion agents. We discuss how we can use the Buckingham Pi theorem, a key tool in dimensional analysis, to provide guidance on the nature and structure of scaling relationships in agent-based models.