This paper proposes a method of assigning trips to automated taxis (ATs) and designing the routes of those vehicles in an urban road network, and also considering the traffic congestion caused by this dynamic responsive service. The system is envisioned to provide a seamless door-to-door service within a city area for all passenger origins and destinations. An integer programming model is proposed to define the routing of the vehicles according to a profit maximization function, depending on the dynamic travel times, which varies with the ATs’ flow. This will be especially important when the number of automated vehicles (AVs) circulating on the roads is high enough that their routing will cause delays. This system should be able to serve not only the reserved travel requests, but also some real-time requests. A rolling horizon scheme is used to divide one day into several periods in which both the real-time and the booked demand will be considered together. The model was applied to the real size case study city of Delft, the Netherlands. The results allow assessing of the impact of the ATs movements on traffic congestion and the profitability of the system. From this case-study, it is possible to conclude that taking into account the effect of the vehicle flows on travel time leads to changes in the system profit, the satisfied percentage and the driving distance of the vehicles, which highlights the importance of this type of model in the assessment of the operational effects of ATs in the future.