Paging with dynamic memory capacity

TL;DR

This paper investigates how dynamic memory capacity affects online paging algorithms, revealing that classic algorithms like LRU remain effective even under adversarial capacity fluctuations, challenging assumptions about the importance of predicting memory changes.

Contribution

It provides a theoretical analysis of paging algorithms under variable memory capacity, showing that some classic algorithms maintain near-optimal performance despite capacity fluctuations.

Findings

LFD achieves minimal page faults even with changing capacity.

Classic algorithms like LRU have near-optimal competitive ratios under dynamic capacity.

Memory prediction is less critical than access pattern prediction for paging performance.

Abstract

We study a generalization of the classic paging problem that allows the amount of available memory to vary over time - capturing a fundamental property of many modern computing realities, from cloud computing to multi-core and energy-optimized processors. It turns out that good performance in the "classic" case provides no performance guarantees when memory capacity fluctuates: roughly speaking, moving from static to dynamic capacity can mean the difference between optimality within a factor 2 in space and time, and suboptimality by an arbitrarily large factor. More precisely, adopting the competitive analysis framework, we show that some online paging algorithms, despite having an optimal (h,k)-competitive ratio when capacity remains constant, are not (3,k)-competitive for any arbitrarily large k in the presence of minimal capacity fluctuations. In this light it is surprising that several classic paging algorithms perform remarkably well even if memory capacity changes adversarially - even without taking those changes into explicit account! In particular, we prove that LFD still achieves the minimum number of faults, and that several classic online algorithms such as LRU have a "dynamic" (h,k)-competitive ratio that is the best one can achieve without knowledge of future page requests, even if one had perfect knowledge of future capacity fluctuations (an exact characterization of this ratio shows it is almost, albeit not quite, equal to the "classic" ratio k/(k-h+1)). In other words, with careful management, knowing/predicting future memory resources appears far less crucial to performance than knowing/predicting future data accesses.