Propagation of Densities of Streaming Data within Query Graphs

Data Stream Systems (DSSs) use cost models to determine if a DSS can cope with a given workload and to optimize query graphs. However, certain relevant input parameters of these models are often unknown or highly imprecise. Especially selectivities are stream-dependent and application-specific parameters. In this paper, we describe a method that supports selectivity estimation considering input streams' attribute value distribution. The novelty of our approach is the propagation of the probability distributions through the query graph in order to give estimates for the inner nodes of the graph. For most common stream operators, we establish formulas that describe their output distribution as a function of their input distributions. For unknown operators like User-Defined Operators (UDOs), we introduce a method to measure the influence of these operators on arbitrary probability distributions. This method is able to do most of the computational work before the query is deployed and introduces minimal overhead at runtime. Our evaluation framework facilitates the appropriate combination of both methods and allows to model almost arbitrary query graphs.