In this paper, we address the problem of serving people by a set of mobile robots. As people move we model this problem as a dynamic patrolling task, that we call the robot-waiters problem. We propose different criteria and metrics suitable to this problem, by considering not only the time to patrol all the people but also the equity of the delivery. We propose and compare four algorithms, two are based on standard solutions to the static patrolling and two are defined according the specificity of patrolling moving entities. The last one introduces a clustering heuristic to identify groups among the people, in order to limit the robots traveled distances. We present a simulator combining a pedestrian model and a robotic model. Experimental results show the efficiency of the specific new approaches. We also discuss the influence of the number of robots on the performances.