Determining Hit Ratios for Multilevel Hierarchies

Introduction As computing grows increasingly more data oriented, the speed of data handling, and especially of storage functions, becomes the limiting factor in the overall performance of modern computers. Storage systems typically use several technologies, which are linked together with the objective of effectively utilizing the advantages of each technology (high speed, low cost). Designing optimal storage hierarchies is rather complicated, not only because of the high dimensionality of the mathematical problems associated with optimization, but also because of the ever changing technology and workload environments. Information available on technology, costs, workload, and performance requirements (the designer’s input) is often of limited accuracy and representativeness. For all these reasons, it is desirable to develop efficient and easily automated storage system design methods to allow the exploration of as many design options as possible. Stack processing introduced by Mattson, et a1 [ 11 has been frequently applied and has also generated some theoretical interest, e.g., in the areas of reference trace analysis and theory of replacement algorithms. This paper presents an outgrowth of standard stack processing, extending its applicability to a realistic class of storage hierarchies, called staging hierarchies by Slutz and Traiger [ 2 ] , who originally described them. Staging hierarchies allow for an arbitrary number of memory levels, using different block sizes at various levels, and for multiple copies of the same block in the system. This paper reviews some earlier results, presenting them from a perspective intended to facilitate understanding of the new extensions to stack processing. These new contributions include the following main results. Abstract: The applicability of stack processing for evaluation of storage hierarchies has been limited to two-level systems and to a very special group of multilevel hierarchies. A generalization of stack processing, called joint stack processing, is introduced. This technique makes possible the efficient determination of hit ratios for a class of multilevel hierarchies staging hierarchies. These hierarchies are rather realistic in the sense that they allow for multiple block sizes and multiple copies of data in the hierarchy. Properties of storage management schemes that lend themselves to ioint stack processing are studied, and the notion of distributed hierarchy