Data stream systems have to deal with massive data volumes. To perform several queries in parallel or to perform even a single query, resources must be planned carefully and the resulting quality-of-service (QoS) is lower than the best one. Typical QoS measures are the output delay and the amount of data in the stream used for the processing. In this paper, we introduce a model which allows to describe stream operators and the streams between the operators of an operator graph belonging to a stream query. The model allows us to calculate the resources consumed by a query graph given a certain result quality. Furthermore, it can be used to determine in advance if the quality-of-service requirement of a given query can be met with the actual available system resources. This model is the basis for building QoS-guaranteeing systems.