The current Internet design is based on a best-effort service, which combines high utilization of network resources with architectural simplicity. As a consequence of this design, the Internet is unable to provide guaranteed or predictable quality of service (QoS) to real-time services that have constraints on end-to-end delay, delay jitter and packet loss. To add QoS capabilities to the present Internet, the new functions need to be simple to implement, while allowing high network utilization. In recent years, different methods have been investigated to provide the required QoS. Most of these methods include some form of admission control so that new flows are only admitted to the network if the admission does not decrease the quality of connections that are already in progress below some defined level. To achieve the required simplicity a new family of admission control methods, called end-to-end measurement-based admission control moves the admission decision to the edges of the network. This thesis presents a set of methods for admission control based on measurements of packet loss. The thesis studies how to deploy admission control in an incremental way: First, admission control is included in the audiovisual real-time applications, without any support from the network. Second, admission control is enabled at the transport layer to differentiate between elastic and inelastic flows, by embedding the probing mechanism in UDP and using the inherent congestion control of TCP. Finally, admission control is deployed at the network layer by providing differentiated scheduling in the network for probe and data packets, which then allows the operator to control the blocking probability for the inelastic flows and the average throughput for the elastic flows. The thesis offers a description of the incremental steps to provide QoS on a DiffServ-based Internet. It analyzes the proposed schemes and provides extensive figures of performance based on simulations and on real implementations. It also shows how the admission control can be used in multicast sessions by making the admission decision at the receiver. The thesis provides as well two different mathematical analyses of the network layer admission control, which enable operators to obtain initial configuration parameters for the admission decision, like queue sizes, based on the forecasted or measured traffic volume. The thesis ends by considering a new method for overload control in WLAN cells, closely based on the ideas for admission control presented in the rest of the articles. / QC 20100826