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This paper proposes the use of an on-demand, ride hailed and ride-Shared Autonomous Vehicle (SAV) service as a feasible solution to serve the mobility needs of a small city where fixed route, circulator type public transportation may be too expensive to operate. The presented work builds upon our earlier work that modeled the city of Marysville, Ohio as an example of such a city, with realistic traffic behavior, and trip requests. A simple SAV dispatcher is implemented to model the behavior of the proposed on-demand mobility service. The goal of the service is to optimally distribute SAVs along the network to allocate passengers and shared rides. The pickup and drop-off locations are strategically placed along the network to provide mobility from affordable housing, which are also transit deserts, to locations corresponding to jobs and other opportunities.