In this paper we present a theoretical framework for the network design with delay QoS guarantee to a voice at the packet level. Especially, we propose a method for estimating the bandwidth at the ingress edge routers accommodating the voice connections and data sessions in the next-generation If network. First, we describe network architecture for VoIP (Voice over IP) services in the NGN (Next Generation Network). After that, we propose a procedure for dimensioning the bandwidth at the output port of a router that accommodates voice and data traffic using the non-preemptive queuing system with strict priority service scheme. Via numerical experiments we illustrate the implication of the proposition.