Dynamic memory allocation systems for minimizing internal fragmentation

Abstract

We have seen that it is possible in a paging environment to decrease internal fragmentation by selecting a variety of page sizes. On most computers page sizes are large to make efficient use of transfer rates between main memory and the external storage medium. On the Atlas we find a page size of 512 words, on the IBM 370 one of 2048, and on the Spectra 70/46 one of 2048. The Honeywell 645 with the Multics system has two page sizes-a small one of 64 words and a large one of 1024 words. (Although the hardware supports the two page sizes, the referee informs us that the software makes use of only the larger.) Evidently, the advantages of using a single, large page size outweigh the cost of internal fragmentation. However, we suspect that there are situations in which the opposite is true. A study of the Burroughs B5500 at the University of Virginia [1] reports that two-thirds of the segment request sizes were under 30 words and half were under 20 words. Such small segment sizes are probably a result of the nature of Algol programs, the hardware of the Burrroughs machine, and the type of jobs run in the university environment. Denning [2] shows that the optimal page size is approximately (Equation presented) where s0 is the average request size, c1 is the cost of losing a word to page tables, and c2 is the cost of losing a word to internal fragmentation. If c1/c2 is small compared to s0, then the optimal page size is also small in relation to s0. If it should become feasible to support a variety of block sizes, then the results in this paper provide the basis for a dynamic memory allocation scheme. The system could monitor its own request distribution and select a collection of page sizes to minimize an appropriate cost function.