The following paper analyzes the operation of autonomous vehicles (AVs) in a private and shared scenario as well the influence of adding a toll in the main bridge that connects a residential area to the city center, representing a case study of the city of Florianópolis in Brazil. We develop a mathematical model whereby the aim is to minimize the overall generalized costs and evaluate its effect on the congestion problem. The main aim of this paper is to estimate some of the impacts that can come up from the deployment of AVs in this urban area where costs of operation, parking and toll are considered and minimized. Several penetration rates of AVs with different shares of private-owned and shared vehicles are analyzed together with the influence of a toll that affects the trips distribution and congestion depicted by the level of service. The main conclusion is that effects on congestion, that can be depicted through the level of service, will only be noticeable when a toll is added and AVs represent a vast majority of the vehicle fleet and some of them are not-private owned, i.e., are shared vehicles. A level of service A will likely be obtained once there is a penetration rate of 50% and 80% of these AVs are shared. When AVs are 80% of the vehicle fleet, 50% of these shall be used for shared purposes. These results can only be obtained if a toll is added to the bridge, that will increase the travel costs and likely force passengers to change their travel behavior.