We propose a new service model based on service curves, which has a loss aspect. In this model, instead of forcing all the packets to meet their deadlines assigned via a service curve, we allow some packets to be dropped. Specifically, the new model is based on guaranteeing at least a certain fraction of the all packets to meet their deadlines assigned via a service curve. The proposed model is composable. We find a necessary and sufficient condition to employ for an efficient Connection Admission Control at a multiplexer to deliver the services according to the new model, via a graph-theoretic approach. A scheduling algorithm to deliver the services as specified by the new service model, at a multiplexer, also exists.