On adequate performance measures for paging

Abstract

Memory management is a fundamental problem in computer architecture and operating systems. We consider a two-level memory system with fast, but small cache and slow, but large main memory. The underlying theoretical problem is known as the paging problem. A sequence of requests to pages has to be served by making each requested page available in the cache. A paging strategy replaces pages in the cache with requested ones. The aim is to minimize the number of page faults that occur whenever a requested page is not in the cache.Experience shows that the paging strategy LEAST-RECENTLY-USED (LRU) usually achieves a factor around 2 to 3 compared to the optimum number of faults. This contrasts the theoretical worst case, in which this factor can be as large as the cache size k.One difficulty in analyzing the paging problem was the lack of an appropriate lower bound for the minimum number of page faults. We address this issue and propose a general lower bound which provides insight into the global structure of a given request sequence. In addition, we derive a characterization for the number of faults incurred by LRU.We give a theoretical explanation why LRU performs well in practice. We classify the set of all request sequences according to certain parameters and prove a bound on the competitive ratio of LRU, which depends on them. This bound varies between 2 and k, i.e., it includes the worst-case, but explains for which sequences LRU achieves constant competitive ratio. The classification is motivated from the structure of request sequences of practical applications: locality of reference and characteristic data access patterns. We argue that this structure yields values around 2 for our bound. Indeed, it is between 2 and 5 in extensive practical experiments.Furthermore, we study the paging problem with variable cache size, which was already considered previously. We show that this approach is not appropriate to explain the usual good performance of LRU. We measure the performance of LRU with the expected competitive ratio E[ALG]/E[OPT] and the expected performance ratio E[ALG]/E[OPT] in a diffuse adversary model and compare both measures. Our analysis yields that the expected competitive ratio gives a misleading answer.