Bandwidth-hungry computer and communication applications, particularly multimedia applications, are rising rapidly. They often require better Quality-of-Service (QoS) than traditional data traffic. Statistical multiplexing and connection admission control (CAC) hold the key to meeting these increasing demands on bandwidth and QoS while making efficient network usage. This monograph starts with an overview of major approaches to CAC. It then focuses on the performance analysis of heterogeneous traffic sources. A number of properties on the multiplexing of heterogeneous sources are established. Based on the above work, a closed-loop architecture is presented that allows CAC to use feedback on the achieved QoS to dynamically adjust its control parameters to achieve more efficient network usage while meeting QoS. The techniques presented can be readily applied in a number of networks, including ATM networks, MPLS networks, cellular networks and WLANs. They are important steps towards more efficient network usage and better QoS, and are especially useful for network managers, researchers, and those who would like to learn about the field.