LRU IS BEITER THAN FIFO UNDER THE INDEPENDENT REFERENCE MODEL J. VAN DEN BERG,* CWI A. GANDOLFI,** Courant Institute Abstract J. Appl. Prob. 29, 239-243 (1992) Printed in Israel Probability Trust 1992 Consider a two-level storage system operating with the least recently used (LRU) or the first-in, first-out (FIFO) replacement strategy. Accesses to the main storage are described by the independent reference model (IRM). Using the FKG inequality, we prove that the miss ratio for LR U is smaller than or equal to the miss ratio for FIFO. REPLACEMENT ALGORITHMS; FKG INEQUALITY; MEMORY MANAGEMENT; MISS RATIO; FIFO; LRU AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60COS SECONDARY 90BOS; 60K99 1. Introduction Consider a storage system which consists of two levels, named main storage and secondary storage. Suppose there are n items, denoted by l, 2, · · ·, n, which can be located in secondary or main storage. The main storage can contain at most m items. Items never leave the system and no new items enter the system. If an item is required, first the main storage is inspected. If it is not present there, it is taken from secondary storage and put in main storage. If the main storage is already full, an item is removed to secondary storage according to some replacement algorithm. This situation occurs for instance in computer systems with paged main and secondary memory (see e.g. Matick (1977)). We restrict our attention to the well-known least recently used (LR U) and first-in, first-out (FIFO) algorithms. In the case of FIFO, that item is replaced which has been in main storage for the longest time. In the case of LRU that item is replaced whose last reference was earliest among those items in main storage. Furthermore we assume that Received 5 November 1990. * Postal address: CWI, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands. Research carried out while the was visiting Cornell University, Ithaca, NY, and partly supported by the US Army Researcli Office. · *"' Present address: Department of Statistics, 367 Evans Hall, University of California, Berkeley, CA 94 720, USA. Research carried out while the author was visiting the University of California at Davis. 239