Under active research, technology of autonomous vehicles (AVs) is getting mature and many AVs will run on the roads in the near future. With the support of vehicular ad-hoc network, AVs become connected. The ability of high degree of control allows AVs to respond to instantaneous situations cooperatively with high efficiency and flexibility. In this paper, we propose a new public transport offering point-to-point services with ride sharing. It manages a fleet of AVs to accommodate a number of transportation requests. Due to the unmanned nature, AVs operate by following the routes instructed by the control center of the system. With proper scheduling, the control center assigns the transportation requests to appropriate AVs in order to minimize the total operational cost. We formulate the scheduling problem with a mixed-integer program. We study the system performance with a typical artificial scenario. Our results show that ride sharing can effectively lower the operational cost and an increase of the vehicular capacity can further enhance the system performance.