The term "Mobility" is gaining new perspectives. Due to the paradigm shift driven by information technologies and autonomous vehicles, on-demand mobility services have experienced significant growth. Operating such a service efficiently is a challenging task. Especially, assigning vehicles to customers plays a vital role in this regard. To meet a satisfactory level of service while keeping the operational costs to a minimum requires efficient assignment strategies. Work summarized in this paper utilizes several shared and non-shared assignment algorithms in order to propose a methodology to assess the effects on the overall system performance for an Autonomous Mobility on Demand system. Selected algorithms are tested in a theoretical network with real-world taxi data with the help of microscopic traffic simulation software Simulation of Urban Mobility. Simulation scenarios are generated for both varying demand levels and increasing fleet sizes. Results suggest that for high demand levels and small fleet sizes, shared algorithms outperform non-shared algorithms for every performance measure chosen: total vehicle kilometers traveled, the ratio of empty fleet kilometers, average passenger waiting time for pick up, and the number of customers served in a period.