Central to the viability of providing traditional services over IP networks is the capability to deliver some level of end-to-end Quality of Service (QoS) to the applications and users. IP networks continue to struggle to migrate from a cost effective best effort data service solution to revenue generating solutions for QoS-sensitive applications such as voice and real-time video. For the case of a network of Media Gateways controlled by SoftSwitches, we propose the use of a measurement based call admission control algorithm at the edge of the network as an approach to provide a cost effective QoS solution. The proposed method utilizes statistical prediction techniques based on available performance measurements without complex QoS management of the packet network. Simulation analysis shows that significant gains in QoS can be achieved with such an edge-to-edge measurement based approach.