Exploring and analyzing large volumes of data plays an increasingly important role in many domains of scientific research. We have been developing the Active Data Repository (ADR), an infrastructure that integrates storage, retrieval, and processing of large multi-dimensional scientific datasets on distributed memory parallel machines with multiple disks attached to each node. In earlier work, we proposed three strategies for processing range queries within the ADR framework. Our experimental results show that the relative performance of the strategies changes under varying application characteristics and machine configurations. In this work we describe analytical models to predict the average computation, I/O and communication operation counts of the strategies when input data elements are uniformly distributed in the attribute space of the output dataset, restricting the output dataset to be a regular d-dimensional array. We validate these models for various synthetic datasets and for several driving applications. Also cross-referenced as UMIACS-TR-99-54