The accelerating emergence of vehicle automation and the anticipation of the advent of shared mobility through fully autonomous vehicles indicate the beginning of a new era of mobility which has the potential to reshape the future of transport in urban areas. In light of such developments, it is important that communities prepare to adapt to the changes they might entail. Therefore, in this paper, traffic flow theory, simulation-based dynamic traffic assignment, and a computer experiment using PTV Visum software were employed to study the impact of different market penetration rates of shared autonomous vehicles (SAVs) on a city-size traffic system. The city of Budapest during morning peak period was chosen as a case study, and a simulation model was created by incorporating SAV elements and their interrelationships into the existing traffic model of the case study city; three alternative future penetration rates were examined in relation to five key performance indicators (KPIs). The simulation results indicated that the implementation of the SAV system has a positive effect on traffic performance. Based on the relationships between the modeled SAV demand shares and the network’s KPIs in the designed scenarios, the overall network performance showed improvement along with an increase in the SAV demand share.