Automated vehicles used as public transport show a great promise of revolutionizing current transportation systems. Still, there are many questions as to how these systems should be organized and operated in cities to bring the best out of future services. In this study, an agent-based model (ABM) is developed to simulate the on-demand operations of shared automated vehicles (SAVs) in a parallel transit service (PTS) and a tailored time-varying transit service (TVTS). The proposed TVTS system can switch service schemes between a door-to-door service (DDS) and a station-to-station service (SSS) according to what is best for the service providers and the travelers. In addition, the proposed PTS system that allows DDS and SSS to operate simultaneously is simulated. To test the conceptual design of the proposed SAV system, simulation experiments are performed in a hypothetical urban area to show the potential of different SAV schemes. Simulation results suggest that SAV systems together with dynamic ridesharing can significantly reduce average waiting time, the vehicle kilometres travelled and empty SAV trips. Moreover, the proposed optimal vehicle assignment algorithm can significantly reduce the empty vehicle kilometres travelled (VKT) for the pickups for all tested SAV systems up to about 40% and improve the system capacity for transporting the passengers. Comparing the TVTS system, which has inconvenient access in peak hours, with the PTS systems, which always makes available door-to-door transport, we conclude that the latter could achieve a similar system performance as the former in terms of average waiting time, service time and system capacity.