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We consider the car following problem for a set of autonomous vehicles following each other on either an infinite or circular road. The behavior of each car is specified by its "speed regulator", a device that decides to increase or decrease the speed of the car as a function of the head-tail distance to its predecessor and the speed of both cars. A collective behavior emerges that corresponds to previously proposed cellular automata traffic models. We further analyze the traffic patterns of the system in the long term, as governed by the speed regulator and we study under which conditions traffic patterns of maximum flow can or cannot be reach. We show the existence of suboptimal flow conditions that require external coordination mechanisms (that we do not consider in this paper) in order to reach the optimal flow achievable with the given density. In contrast with other approaches, we do not try to reproduce observed or measured traffic patterns. We analyze a deterministic speed regulator in order to decipher the emergent dynamics, and to ponder what maneuvers can be safely performed. Here, we restrict our attention to the car following problem. By comparing our speed regulator with classical models, auch as the Nagel–Schreckenberg and KKW models, we observe that although our regulator is formulated in simple terms, its dynamics share similarities with these models. In particular, the KKW model is designed to reproduce the observed behavior that a trailing car in the synchronization range of the leading car tends to regulate its speed to maintain a constant distance. this same behavior is adopted by our speed regulator, showing that this is a safe way of driving. [ABSTRACT FROM AUTHOR]