The problem of network bandwidth limitations is encountered in almost any distributed virtual environment or networked game. In a typical client-server setup, where the virtual world is managed by a server and replicated by connected clients, who visualize the scene, the server must repeatedly transmit update messages to the clients. By employing visibility information, the number of messages transmitted over the network can be reduced by sending each client only update messages for objects, which are visible from the viewpoint of the client.This paper presents a technique that allows the server to manage the transmission of update messages for each client with a constant overhead, reducing overall computational cost to a linear effort. We show how the server can employ visibility information to schedule all objects using the priority Round-Robin algorithm. This algorithm is further enhanced with activity monitoring that provides a graceful degradation of the system's performance, even if the behavior of objects is unpredictable. This makes the algorithm suited to schedule update messages regarding server-controlled objects as well as user-controlled avatars.