The efficient management of interval data represents a core requirement for many temporal and spatial database applications. With the Relational Interval Tree (RI-tree1 ), an efficient access method has been proposed to process interval intersection queries on top of existing objectrelational database systems. This paper complements that approach by effective and efficient models to estimate the selectivity and the I/O cost of interval intersection queries in order to guide the cost-based optimizer whether and how to include the RI-tree into the execution plan. By design, the models immediately fit to common extensible indexing/ optimization frameworks, and their implementations exploit the built-in statistics facilities of the database server. According to our experimental evaluation on an Oracle database, the average relative error of the estimated cost to the actual cost of index scans ranges from 0% to 23%, depending on the resolution of the persistent statistics and the size of t...