Propeties of storage hierarchy systems with multiple page sizes and redundant data

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Abstract
The need for high performance, highly reliable storage for very large on-line databases, coupled with rapid advances in storage device technology, has made the study of generalized storage hierarchies an important area of research. This paper analyzes properties of a data storage hierarchy system specifically designed for handling very large on-line databases. To attain high performance and high reliability, the data storage hierarchy makes use of multiple page sizes in different storage levels and maintains multiple copies of the same information across the storage levels. Such a storage hierarchy system is currently being designed as part of the INFOPLEX database computer project. Previous studies of storage hierarchies have primarily focused on virtual memories for program storage and hierarchies with a single page size across all storage levels and/or a single copy of information in the hierarchy. In the INFOPLEX design, extensions to the least recently used (LRU) algorithm are used to manage the storage levels. The read-through technique is used to initially load a referenced page of the appropriate size into all storage levels above the one in which the page is found. Since each storage level is viewed as an extension of the immediate higher level, an overflow page from level i is always placed in level i + 1. Important properties of these algorithms are derived. It is shown that depending on the types of algorithms used and the relative sizes of the storage levels, it is not always possible to guarantee that the contents of a given storage level i is always a superset of the contents of its immediate higher storage level i - 1. The necessary and sufficient conditions for this property to hold are identified and proved. Furthermore, it is possible that increasing the size of intermediate storage levels may actually increase the number of references to lower storage levels, resulting in reduced performance. Conditions necessary to avoid such an anomaly are also identified and proved.