The issue of converged networks is to ensure the sufficient quality of services along the entire length of the communication transmission. This issue is closely connected to the real-time services, such as VoIP (Voice over Internet Protocol) and videoconferencing. These services require strict adherence to quality parameters, otherwise their function is not guaranteed. This problem particulary resolves subsystem IMS (IP Multimedia Subsystem), which concluded on the basis of user profiles can provide the required quality of service. Therefore the theoretical part deals with the description of the structure of the system and protocols designed to signal the network. Various mechanisms to support quality of services in access and backbone networks are also described. The following section explains the principle of provision of quality requirements of end-user networks. In the practical part is this theoretical knowledge used for designing and configuration of the network consisting of various technologies. The resulting model is then simulated in Opnet Modeler program, which is used for designing and testing of packet networks. Each simulation shows the effect of mapping quality requirements in the different access network on technologies, which are supported in the backbone. The outcome of this work is detailed network analysis and comparison of mechanisms for implementing quality of service. The conclusion summarises all simulation outcomes.