We design controllers and derive implementable algorithms for autonomous and cooperative car-following control (CFC) systems under a receding horizon control framework. An autonomous CFC system controls vehicle acceleration to optimize its own situation, whereas a cooperative CFC (C-CFC) system coordinates accelerations of cooperative vehicles to optimize the joint situation. To realize simultaneous control of many vehicles in a traffic system, decentralized and distributed algorithms are implemented in a microscopic traffic simulator for CFC and C-CFC controllers, respectively. The impacts of the proposed controllers on dynamic traffic flow features, particularly on formation and propagation of moving jams, are investigated through a simulation on a two-lane freeway with CFC/C-CFC vehicles randomly distributed. The simulation shows that the proposed decentralized CFC and distributed C-CFC algorithms are implementable in microscopic simulations, and the assessment reveals that CFC and C-CFC systems change moving jam characteristics substantially.