Generalized processor sharing (GPS) is a scheduling discipline which provides minimum service guarantees as well as fair resource sharing. The performance of GPS is governed by the scheduling weights associated with individual connections. We address the design of the GPS weights, along with the related connection admission control (CAC). Our main goal is to achieve statistical multiplexing gains in the presence of multiple traffic and quality-of-service (QoS) classes of connections that share a common trunk. We present novel techniques to compute and adapt the weights. We also characterize the capacity region of the system, and propose a natural CAC procedure. Numerical results on 2-class and 3-class examples demonstrate the effectiveness of our methods.