We describe a Digital Advertising System Simulation (DASS) for modeling advertising and its impact on user behavior. DASS is both flexible and general, and can be applied to research on a wide range of topics, such as digital attribution, ad fatigue, campaign optimization, and marketing mix modeling. This paper introduces the basic DASS simulation framework and illustrates its application to digital attribution. We show that common position-based attribution models fail to capture the true causal effects of advertising across several simple scenarios. These results lay a groundwork for the evaluation of more complex attribution models, and the development of improved models.