We investigate the QoS-based classification of traffic streams for a multi-class link model with predetermined service levels. Specifically, we consider a link model with fixed service levels or fixed class weights which may be represented by a finite number of MPLS Label-Switched-Paths (LSPs). Our target is to classify a set of traffic streams each with arbitrary local QoS-demand into a small number of service levels while optimizing the residual-allocatedresources as a result of the traffic classification. The residual-allocated-resources will be measured by the service-quantization-overhead which is the summation of the differences between the required QoS and the offered service level for all traffic streams. We formulate the classification as a Dynamic- Programming problem. We then present a group of polynomial-time-algorithms to obtain the optimal classification for soft and hard QoS requirements. We also present the concept of "differentiation factor" and show the effect of this factor on minimizing the quantization-overhead.