Motivated by the presence and significant growth of mobility-on-demand (MOD) services provided by Transportation Network Companies in cities, over the past 6-7 years researchers have made significant advancements modeling MOD and automated MOD (AMOD) vehicle fleets. One stream of research has focused on optimizing fleet performance via developing smart (model-based) control policies and solution algorithms. A second stream of research has focused on integrating 'reasonable' but operationally inefficient MOD vehicle fleet models into transportation system simulation models to analyze their potential transportation system impacts (e.g. congestion, mode choice, destination choice, accessibility, emissions, etc.) and to do policy analysis. The scalability of the former set of MOD fleet models and control policies to very large vehicle fleets is questionable at best; whereas, the fleet performance of the latter set of MOD vehicle fleet models is typically poor. Hence, the goal of this research is to develop MOD fleet models and control policies that are computationally efficient yet reasonably resemble a MOD fleet operator focused on optimizing operational performance. To meet this goal, this study presents several modeling strategies that significantly reduce the computational complexity of the vehicle-traveler assignment problem, while not degrading the MOD fleet performance. The modeling strategies take advantage of the known spatial distribution of travelers and available vehicles at each time step. Computational results in medium (e.g. Bloomington, IN, USA) and large (e.g. Chicago, IL, USA) size cities/networks illustrate the very large computational benefits and the significant fleet performance benefits of the proposed strategies. The presentation will discuss the modeling details as well as how these models can be used to help cities make infrastructure investments and policy decisions -- the focus of an ongoing NSF research project.