Effect of Replacement Algorithms on a Paged Buffer Database System

In a database system a buffer may be used to hold recently referenced pages. If this buffer is in virtual memory, the database paging system and the memory paging system affect its performance. The study of the effect of main memory replacement algorithms on the number of main memory page faults is the basic objective of this paper. We assume that the buffer replacement algorithm is least recently used (LRU), and page fault rates for LRU, random (R), and generalized least recently used (GLRU) main memory replacement algorithms are calculated and compared. A set of experiments validates these fault rate expressions and establishes some conditions for the practical application of the results. Introduction An important aspect of the performance analysis of a data management system (DMS) is the behavior of the buffer where previously referenced pages are held for possible future reference. If the DMS executes in a virtual memory system the buffer is in the virtual address space and, at a given time, some of the buffer pages are also in real storage. Two paging mechanisms participate in the process of accessing a database page, a DMS-controlled buffer paging and a virtual memory paging under the control of the operating system. This structure is of practical importance since it represents the operating environment for IMS and other commercial database systems, and several studies of its behavior have been made. In particular, the effect of the buffer size on performance has been evaluated analytically by using models that incorporate different assumptions [ 1-31, and also by actual measurement [ l , 2, 4, 51. While the performance of replacement algorithms has been studied analytically for virtual memory systems, for DMS only empirical evaluations have been made [ 2 , 4, 51. The databqse virtual buffer environment is different due both to the presence of two memory levels, and to the different characteristics of the reference strings found in these applications. We analyze here the effect of main memory replacement algorithms on the performance of the buffer system, when the buffer replacement algorithm is LRU (least recently used). In a demand paging environment this performance can be characterized by the number of main memory page faults. If the reference string is described by the least recently used (LRU) stack model [6], known probabilities of reference can be associated with specific positions of the stack. In non-database applications the stack probabilities usually have a decreasing characteristic with respect to stack distance, and for this case the LRU replacement algorithm has been shown to be optimal [7]. However, for database applications the stack probabilities could exhibit a different distribution, and it is shown in [8] that in general the optimal algorithm belongs to a class of which the LRU algorithm is a particular case. This optimal algorithm is denoted here as generalized LRU'(GLRU). Another important replacement algorithm is the random algorithm (R), where the page to be replaced is selected with a uniform probabili(y. These three algorithms (LRU, GLRU, and R) are considered here since they are of practical importance and possess tractable analytical characteristics. The next section presents a model of the buffer system and introduces basic concepts. Models are then developed for the three memory replacement algorithms (LRU, R, and GLRU), and expressions are presented for Copyright 1978 by International Business Machines Corporation. Copying is permitted without payment of royalty provided that (1) each reproduction is done without alteration and (2) theJournal reference and IBM copyright notice are included on the first page. The title and abstract may be used without further permission in computer-based and other information-service systems. Permission to republish other excerpts should be obtained from the Editor. IBM I . RES. DEVELOP. e VOL. 22 NO. 2 e MAR 1978 I 185 'ERNANDEZ, LANG, AND WOOD