Localized Web clusters and geographically dispersed replicated server/cluster architectures are two common architectures employed to improve the performance of an Internet service for the global users of the service. One method of server selection proposed for these architectures is the network-layer anycast method. In this method, a single anycast address is used to represent the collection of replicated servers and a routing protocol is used to route packets to the nearest server. This method has been found to be efficient but performs poorly in heavy load conditions due to its lack of support for quality of service requirements. However, the network-layer anycast method can be effectively implemented to provide quality of service in an active network - a new generation network that deploys programmable 'active routers' to make routing decisions based on information collected and processed within the network. In this paper, we simulate two round-trip-time-based (RTT-based) methods of server selection using the network-layer anycast technique on an active network and compare the performance of this method with the static round-robin server selection technique in a specific network scenario.