On the Smoothness of Paging Algorithms

TL;DR

This paper investigates the smoothness of paging algorithms, establishing bounds and introducing new algorithms that balance smoothness and competitiveness in page fault performance.

Contribution

It provides bounds on the smoothness of deterministic and randomized paging algorithms and introduces Smoothed-LRU and LRU-Random algorithms to improve smoothness.

Findings

LRU matches the lower bound on smoothness among deterministic algorithms.

FIFO matches the upper bound on smoothness among deterministic algorithms.

New algorithms Smoothed-LRU and LRU-Random offer improved smoothness with competitive performance.

Abstract

We study the smoothness of paging algorithms. How much can the number of page faults increase due to a perturbation of the request sequence? We call a paging algorithm smooth if the maximal increase in page faults is proportional to the number of changes in the request sequence. We also introduce quantitative smoothness notions that measure the smoothness of an algorithm. We derive lower and upper bounds on the smoothness of deterministic and randomized demand-paging and competitive algorithms. Among strongly-competitive deterministic algorithms LRU matches the lower bound, while FIFO matches the upper bound. Well-known randomized algorithms like Partition, Equitable, or Mark are shown not to be smooth. We introduce two new randomized algorithms, called Smoothed-LRU and LRU-Random. Smoothed- LRU allows to sacrifice competitiveness for smoothness, where the trade-off is controlled by a parameter. LRU-Random is at least as competitive as any deterministic algorithm while smoother.