Parking is a major constraint for car users and therefore an important factor in mode choice decisions. In this paper we introduce a model to simulate parking search behavior for cars within a multi-agent transport simulation, including full simulation of all steps of parking search, such as walking to and from the vehicle. This is combined with the capabilities of privately owned autonomous vehicles (AVs), which may park automatically, often in other locations than conventional cars, once they are not in use. Three different strategies for AVs to park are developed: (1) Conventional parking search, (2) parking at a designated AV lot, and (3) empty cruising, where vehicles do not use any parking space, but keep on driving. We apply the simulation model to a residential neighborhood in central Berlin, where parking pressure is generally high and apply different shares of AV usage to the synthetic population used. This allows a detailed evaluation of effects for both AV and conventional vehicle owners. Results suggest that the usage of designated parking lots may be the most beneficial solution for most users, with both vehicle wait times and parking search durations being the lowest.