We investigate the problem of stochastic-QoS-based-classification of traffic streams for a multi-class-link-model with predetermined service levels calculated based on the link's total load. Specifically, we consider a link model with fixed service levels 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 requirement, in addition to the bandwidth demand into a small number of service-levels while optimizing the residual-allocated-resources as a result of the traffic classification. The residual-allocated-resources will be measured by the service-quantizationoverhead 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 constrained integer-linear optimization problem. We then present two efficient algorithms based on Branch and Bound technique to obtain the optimal classification for a set of traffic streams for link models with predetermined service levels.